%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN460-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:12 AM UTC 2025
% Result : Unsatisfiable 1.15s 1.31s
% Output : Proof 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN460-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:37:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.15/1.31 % SZS status Unsatisfiable
% 1.15/1.31 % SZS output start Proof
% 1.15/1.31 tff(c3_1_type, type, (
% 1.15/1.31 c3_1: $i > $o)).
% 1.15/1.31 tff(a2252_type, type, (
% 1.15/1.31 a2252: $i)).
% 1.15/1.31 tff(a2190_type, type, (
% 1.15/1.31 a2190: $i)).
% 1.15/1.31 tff(c2_1_type, type, (
% 1.15/1.31 c2_1: $i > $o)).
% 1.15/1.31 tff(c1_1_type, type, (
% 1.15/1.31 c1_1: $i > $o)).
% 1.15/1.31 tff(c0_1_type, type, (
% 1.15/1.31 c0_1: $i > $o)).
% 1.15/1.31 tff(ndr1_0_type, type, (
% 1.15/1.31 ndr1_0: $o)).
% 1.15/1.31 tff(hskp3_type, type, (
% 1.15/1.31 hskp3: $o)).
% 1.15/1.31 tff(a2204_type, type, (
% 1.15/1.31 a2204: $i)).
% 1.15/1.31 tff(hskp40_type, type, (
% 1.15/1.31 hskp40: $o)).
% 1.15/1.31 tff(a2228_type, type, (
% 1.15/1.31 a2228: $i)).
% 1.15/1.31 tff(hskp48_type, type, (
% 1.15/1.31 hskp48: $o)).
% 1.15/1.31 tff(a2189_type, type, (
% 1.15/1.31 a2189: $i)).
% 1.15/1.31 tff(hskp34_type, type, (
% 1.15/1.31 hskp34: $o)).
% 1.15/1.31 tff(hskp46_type, type, (
% 1.15/1.31 hskp46: $o)).
% 1.15/1.31 tff(a2242_type, type, (
% 1.15/1.31 a2242: $i)).
% 1.15/1.31 tff(a2218_type, type, (
% 1.15/1.31 a2218: $i)).
% 1.15/1.31 tff(a2186_type, type, (
% 1.15/1.31 a2186: $i)).
% 1.15/1.31 tff(hskp32_type, type, (
% 1.15/1.31 hskp32: $o)).
% 1.15/1.31 tff(hskp18_type, type, (
% 1.15/1.31 hskp18: $o)).
% 1.15/1.31 tff(a2188_type, type, (
% 1.15/1.31 a2188: $i)).
% 1.15/1.31 tff(hskp33_type, type, (
% 1.15/1.31 hskp33: $o)).
% 1.15/1.31 tff(a2181_type, type, (
% 1.15/1.31 a2181: $i)).
% 1.15/1.31 tff(a2215_type, type, (
% 1.15/1.31 a2215: $i)).
% 1.15/1.31 tff(hskp44_type, type, (
% 1.15/1.31 hskp44: $o)).
% 1.15/1.31 tff(a2222_type, type, (
% 1.15/1.31 a2222: $i)).
% 1.15/1.31 tff(hskp53_type, type, (
% 1.15/1.31 hskp53: $o)).
% 1.15/1.31 tff(a2235_type, type, (
% 1.15/1.31 a2235: $i)).
% 1.15/1.31 tff(hskp0_type, type, (
% 1.15/1.31 hskp0: $o)).
% 1.15/1.31 tff(a2226_type, type, (
% 1.15/1.31 a2226: $i)).
% 1.15/1.31 tff(a2187_type, type, (
% 1.15/1.31 a2187: $i)).
% 1.15/1.31 tff(hskp58_type, type, (
% 1.15/1.31 hskp58: $o)).
% 1.15/1.31 tff(hskp21_type, type, (
% 1.15/1.31 hskp21: $o)).
% 1.15/1.31 tff(hskp55_type, type, (
% 1.15/1.31 hskp55: $o)).
% 1.15/1.31 tff(hskp54_type, type, (
% 1.15/1.31 hskp54: $o)).
% 1.15/1.31 tff(hskp2_type, type, (
% 1.15/1.31 hskp2: $o)).
% 1.15/1.31 tff(hskp47_type, type, (
% 1.15/1.31 hskp47: $o)).
% 1.15/1.31 tff(a2200_type, type, (
% 1.15/1.31 a2200: $i)).
% 1.15/1.31 tff(hskp38_type, type, (
% 1.15/1.31 hskp38: $o)).
% 1.15/1.31 tff(hskp37_type, type, (
% 1.15/1.31 hskp37: $o)).
% 1.15/1.31 tff(a2198_type, type, (
% 1.15/1.31 a2198: $i)).
% 1.15/1.31 tff(hskp7_type, type, (
% 1.15/1.31 hskp7: $o)).
% 1.15/1.31 tff(a2197_type, type, (
% 1.15/1.31 a2197: $i)).
% 1.15/1.31 tff(hskp6_type, type, (
% 1.15/1.31 hskp6: $o)).
% 1.15/1.31 tff(a2196_type, type, (
% 1.15/1.31 a2196: $i)).
% 1.15/1.31 tff(a2240_type, type, (
% 1.15/1.31 a2240: $i)).
% 1.15/1.31 tff(a2241_type, type, (
% 1.15/1.31 a2241: $i)).
% 1.15/1.31 tff(hskp26_type, type, (
% 1.15/1.31 hskp26: $o)).
% 1.15/1.31 tff(a2178_type, type, (
% 1.15/1.31 a2178: $i)).
% 1.15/1.31 tff(a2239_type, type, (
% 1.15/1.31 a2239: $i)).
% 1.15/1.31 tff(hskp17_type, type, (
% 1.15/1.31 hskp17: $o)).
% 1.15/1.31 tff(a2221_type, type, (
% 1.15/1.31 a2221: $i)).
% 1.15/1.31 tff(a2206_type, type, (
% 1.15/1.31 a2206: $i)).
% 1.15/1.31 tff(hskp10_type, type, (
% 1.15/1.31 hskp10: $o)).
% 1.15/1.31 tff(a2191_type, type, (
% 1.15/1.31 a2191: $i)).
% 1.15/1.31 tff(hskp4_type, type, (
% 1.15/1.31 hskp4: $o)).
% 1.15/1.31 tff(a2205_type, type, (
% 1.15/1.31 a2205: $i)).
% 1.15/1.31 tff(hskp41_type, type, (
% 1.15/1.31 hskp41: $o)).
% 1.15/1.31 tff(a2185_type, type, (
% 1.15/1.31 a2185: $i)).
% 1.15/1.31 tff(hskp31_type, type, (
% 1.15/1.31 hskp31: $o)).
% 1.15/1.31 tff(hskp56_type, type, (
% 1.15/1.31 hskp56: $o)).
% 1.15/1.31 tff(1,plain,
% 1.15/1.31 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))))),
% 1.15/1.31 inference(bind,[status(th)],[])).
% 1.15/1.31 tff(2,plain,
% 1.15/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[1])).
% 1.15/1.32 tff(3,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(4,plain,
% 1.15/1.32 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(5,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[4])).
% 1.15/1.32 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause290')).
% 1.15/1.32 tff(7,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.15/1.32 tff(8,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.15/1.32 tff(9,plain,(
% 1.15/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.15/1.32 inference(skolemize,[status(sab)],[8])).
% 1.15/1.32 tff(10,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.15/1.32 tff(11,plain,
% 1.15/1.32 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(12,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[11])).
% 1.15/1.32 tff(13,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(14,plain,
% 1.15/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(15,plain,
% 1.15/1.32 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[14])).
% 1.15/1.32 tff(16,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(U)) | c1_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause273')).
% 1.15/1.32 tff(17,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.15/1.32 tff(18,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.15/1.32 tff(19,plain,(
% 1.15/1.32 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.15/1.32 inference(skolemize,[status(sab)],[18])).
% 1.15/1.32 tff(20,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.15/1.32 tff(21,assumption,(c3_1(a2252)), introduced(assumption)).
% 1.15/1.32 tff(22,plain,
% 1.15/1.32 (^[V: $i, U: $i] : refl((hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(23,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[22])).
% 1.15/1.32 tff(24,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(25,plain,
% 1.15/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp40))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp40) <=> (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40) <=> (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(26,plain,
% 1.15/1.32 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[25])).
% 1.15/1.32 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c0_1(U)) | c2_1(V)) | hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause282')).
% 1.15/1.32 tff(28,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.15/1.32 tff(29,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.15/1.32 tff(30,plain,(
% 1.15/1.32 ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.15/1.32 inference(skolemize,[status(sab)],[29])).
% 1.15/1.32 tff(31,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.15/1.32 tff(32,plain,
% 1.15/1.32 (^[V: $i, U: $i] : refl((hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(33,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[32])).
% 1.15/1.32 tff(34,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(35,plain,
% 1.15/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp48))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp48) <=> (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48) <=> (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(36,plain,
% 1.15/1.32 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48) <=> ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[35])).
% 1.15/1.32 tff(37,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(U)) | c0_1(V)) | hskp48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause279')).
% 1.15/1.32 tff(38,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[37, 36])).
% 1.15/1.32 tff(39,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.15/1.32 tff(40,plain,(
% 1.15/1.32 ![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(skolemize,[status(sab)],[39])).
% 1.15/1.32 tff(41,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[40, 33])).
% 1.15/1.32 tff(42,plain,
% 1.15/1.32 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(43,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[42])).
% 1.15/1.32 tff(44,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(45,plain,
% 1.15/1.32 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(46,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[45])).
% 1.15/1.32 tff(47,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause292')).
% 1.15/1.32 tff(48,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.15/1.32 tff(49,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[48, 44])).
% 1.15/1.32 tff(50,plain,(
% 1.15/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 1.15/1.32 inference(skolemize,[status(sab)],[49])).
% 1.15/1.32 tff(51,plain,
% 1.15/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[50, 43])).
% 1.15/1.32 tff(52,plain,
% 1.15/1.32 (^[U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(53,plain,
% 1.15/1.32 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[52])).
% 1.15/1.32 tff(54,plain,
% 1.15/1.32 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(55,plain,
% 1.15/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U)) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U))) | c2_1(U)) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U)) <=> (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(56,plain,
% 1.15/1.32 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U)) <=> ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[55])).
% 1.15/1.32 tff(57,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c3_1(U)) | hskp18) | c2_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause245')).
% 1.15/1.32 tff(58,plain,
% 1.15/1.32 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.15/1.32 tff(59,plain,
% 1.15/1.32 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[58, 54])).
% 1.15/1.32 tff(60,plain,(
% 1.15/1.32 ![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/1.32 inference(skolemize,[status(sab)],[59])).
% 1.15/1.32 tff(61,plain,
% 1.15/1.32 (![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[60, 53])).
% 1.15/1.32 tff(62,plain,
% 1.15/1.32 (^[V: $i, U: $i] : refl((hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(63,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[62])).
% 1.15/1.32 tff(64,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(65,plain,
% 1.15/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | hskp33))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V))) | hskp33) <=> (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33) <=> (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(66,plain,
% 1.15/1.32 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[65])).
% 1.15/1.32 tff(67,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(V))) | c0_1(U)) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause284')).
% 1.15/1.32 tff(68,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.15/1.32 tff(69,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[68, 64])).
% 1.15/1.32 tff(70,plain,(
% 1.15/1.32 ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(skolemize,[status(sab)],[69])).
% 1.15/1.32 tff(71,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[70, 63])).
% 1.15/1.32 tff(72,assumption,(~hskp33), introduced(assumption)).
% 1.15/1.32 tff(73,assumption,(hskp32), introduced(assumption)).
% 1.15/1.32 tff(74,plain,
% 1.15/1.32 (((~hskp32) | c0_1(a2186)) <=> ((~hskp32) | c0_1(a2186))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(75,axiom,((~hskp32) | c0_1(a2186)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.15/1.32 tff(76,plain,
% 1.15/1.32 ((~hskp32) | c0_1(a2186)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.15/1.32 tff(77,plain,
% 1.15/1.32 ((~hskp32) | c0_1(a2186)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[76, 74])).
% 1.15/1.32 tff(78,plain,
% 1.15/1.32 ((~hskp32) | c0_1(a2186)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[77, 74])).
% 1.15/1.32 tff(79,plain,
% 1.15/1.32 ((~hskp32) | c0_1(a2186)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[78, 74])).
% 1.15/1.32 tff(80,plain,
% 1.15/1.32 ((~hskp32) | c0_1(a2186)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[79, 74])).
% 1.15/1.32 tff(81,plain,
% 1.15/1.32 (c0_1(a2186)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[80, 73])).
% 1.15/1.32 tff(82,plain,
% 1.15/1.32 (((~hskp32) | (~c3_1(a2186))) <=> ((~hskp32) | (~c3_1(a2186)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(83,plain,
% 1.15/1.32 (((~c3_1(a2186)) | (~hskp32)) <=> ((~hskp32) | (~c3_1(a2186)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(84,axiom,((~c3_1(a2186)) | (~hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.15/1.32 tff(85,plain,
% 1.15/1.32 ((~hskp32) | (~c3_1(a2186))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.15/1.32 tff(86,plain,
% 1.15/1.32 ((~hskp32) | (~c3_1(a2186))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[85, 82])).
% 1.15/1.32 tff(87,plain,
% 1.15/1.32 (~c3_1(a2186)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[86, 73])).
% 1.15/1.32 tff(88,assumption,(hskp53), introduced(assumption)).
% 1.15/1.32 tff(89,plain,
% 1.15/1.32 (((~hskp53) | c0_1(a2235)) <=> ((~hskp53) | c0_1(a2235))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(90,axiom,((~hskp53) | c0_1(a2235)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.15/1.32 tff(91,plain,
% 1.15/1.32 ((~hskp53) | c0_1(a2235)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.15/1.32 tff(92,plain,
% 1.15/1.32 ((~hskp53) | c0_1(a2235)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[91, 89])).
% 1.15/1.32 tff(93,plain,
% 1.15/1.32 ((~hskp53) | c0_1(a2235)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[92, 89])).
% 1.15/1.32 tff(94,plain,
% 1.15/1.32 ((~hskp53) | c0_1(a2235)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[93, 89])).
% 1.15/1.32 tff(95,plain,
% 1.15/1.32 ((~hskp53) | c0_1(a2235)),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[94, 89])).
% 1.15/1.32 tff(96,plain,
% 1.15/1.32 (c0_1(a2235)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[95, 88])).
% 1.15/1.32 tff(97,assumption,(~c2_1(a2181)), introduced(assumption)).
% 1.15/1.32 tff(98,assumption,(~c1_1(a2181)), introduced(assumption)).
% 1.15/1.32 tff(99,assumption,(~c0_1(a2181)), introduced(assumption)).
% 1.15/1.32 tff(100,assumption,(~hskp32), introduced(assumption)).
% 1.15/1.32 tff(101,assumption,(c3_1(a2181)), introduced(assumption)).
% 1.15/1.32 tff(102,plain,
% 1.15/1.32 (^[V: $i, U: $i] : refl((hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.15/1.32 inference(bind,[status(th)],[])).
% 1.15/1.32 tff(103,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.15/1.32 inference(quant_intro,[status(thm)],[102])).
% 1.15/1.32 tff(104,plain,
% 1.15/1.32 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(105,plain,
% 1.15/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp32))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp32) <=> (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32) <=> (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(106,plain,
% 1.15/1.33 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32) <=> ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[105])).
% 1.15/1.33 tff(107,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause270')).
% 1.15/1.33 tff(108,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.15/1.33 tff(109,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[108, 104])).
% 1.15/1.33 tff(110,plain,(
% 1.15/1.33 ![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(skolemize,[status(sab)],[109])).
% 1.15/1.33 tff(111,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[110, 103])).
% 1.15/1.33 tff(112,plain,
% 1.15/1.33 (^[U: $i] : refl((hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(113,plain,
% 1.15/1.33 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[112])).
% 1.15/1.33 tff(114,plain,
% 1.15/1.33 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(115,plain,
% 1.15/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U))) | hskp58))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U))) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U)) <=> ((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite(((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U))) | c1_1(U)) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U)) <=> (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(116,plain,
% 1.15/1.33 (![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U)) <=> ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[115])).
% 1.15/1.33 tff(117,axiom,(![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c2_1(U)) | hskp58) | c1_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause246')).
% 1.15/1.33 tff(118,plain,
% 1.15/1.33 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.15/1.33 tff(119,plain,
% 1.15/1.33 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[118, 114])).
% 1.15/1.33 tff(120,plain,(
% 1.15/1.33 ![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.15/1.33 inference(skolemize,[status(sab)],[119])).
% 1.15/1.33 tff(121,plain,
% 1.15/1.33 (![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[120, 113])).
% 1.15/1.33 tff(122,assumption,(~ndr1_0), introduced(assumption)).
% 1.15/1.33 tff(123,plain,
% 1.15/1.33 ((ndr1_0 | (~hskp21)) <=> (ndr1_0 | (~hskp21))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(124,plain,
% 1.15/1.33 (((~hskp21) | ndr1_0) <=> (ndr1_0 | (~hskp21))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(125,axiom,((~hskp21) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.15/1.33 tff(126,plain,
% 1.15/1.33 (ndr1_0 | (~hskp21)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.15/1.33 tff(127,plain,
% 1.15/1.33 (ndr1_0 | (~hskp21)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[126, 123])).
% 1.15/1.33 tff(128,plain,
% 1.15/1.33 (~hskp21),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[127, 122])).
% 1.15/1.33 tff(129,plain,
% 1.15/1.33 ((ndr1_0 | (~hskp55)) <=> (ndr1_0 | (~hskp55))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(130,plain,
% 1.15/1.33 (((~hskp55) | ndr1_0) <=> (ndr1_0 | (~hskp55))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(131,axiom,((~hskp55) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 1.15/1.33 tff(132,plain,
% 1.15/1.33 (ndr1_0 | (~hskp55)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[131, 130])).
% 1.15/1.33 tff(133,plain,
% 1.15/1.33 (ndr1_0 | (~hskp55)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[132, 129])).
% 1.15/1.33 tff(134,plain,
% 1.15/1.33 (~hskp55),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[133, 122])).
% 1.15/1.33 tff(135,plain,
% 1.15/1.33 ((ndr1_0 | (~hskp54)) <=> (ndr1_0 | (~hskp54))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(136,plain,
% 1.15/1.33 (((~hskp54) | ndr1_0) <=> (ndr1_0 | (~hskp54))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(137,axiom,((~hskp54) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.15/1.33 tff(138,plain,
% 1.15/1.33 (ndr1_0 | (~hskp54)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.15/1.33 tff(139,plain,
% 1.15/1.33 (ndr1_0 | (~hskp54)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[138, 135])).
% 1.15/1.33 tff(140,plain,
% 1.15/1.33 (~hskp54),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[139, 122])).
% 1.15/1.33 tff(141,plain,
% 1.15/1.33 ((hskp55 | hskp54 | hskp21) <=> (hskp55 | hskp54 | hskp21)),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(142,plain,
% 1.15/1.33 (((hskp21 | hskp54) | hskp55) <=> (hskp55 | hskp54 | hskp21)),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(143,axiom,((hskp21 | hskp54) | hskp55), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.15/1.33 tff(144,plain,
% 1.15/1.33 (hskp55 | hskp54 | hskp21),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.15/1.33 tff(145,plain,
% 1.15/1.33 (hskp55 | hskp54 | hskp21),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[144, 141])).
% 1.15/1.33 tff(146,plain,
% 1.15/1.33 (hskp55 | hskp54 | hskp21),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[145, 141])).
% 1.15/1.33 tff(147,plain,
% 1.15/1.33 (hskp55 | hskp54 | hskp21),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[146, 141])).
% 1.15/1.33 tff(148,plain,
% 1.15/1.33 (hskp55 | hskp54 | hskp21),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[147, 141])).
% 1.15/1.33 tff(149,plain,
% 1.15/1.33 ($false),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[148, 140, 134, 128])).
% 1.15/1.33 tff(150,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.15/1.33 tff(151,plain,
% 1.15/1.33 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(152,plain,
% 1.15/1.33 ((hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181))) <=> (hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(153,plain,
% 1.15/1.33 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[152])).
% 1.15/1.33 tff(154,plain,
% 1.15/1.33 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.15/1.33 inference(transitivity,[status(thm)],[153, 151])).
% 1.15/1.33 tff(155,plain,
% 1.15/1.33 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(156,plain,
% 1.15/1.33 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[155, 154])).
% 1.15/1.33 tff(157,plain,
% 1.15/1.33 (hskp58 | c1_1(a2181) | (~c3_1(a2181))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[156, 150, 97, 121])).
% 1.15/1.33 tff(158,plain,
% 1.15/1.33 (hskp58),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[157, 101, 98])).
% 1.15/1.33 tff(159,plain,
% 1.15/1.33 (((~hskp58) | (~c1_1(a2252))) <=> ((~hskp58) | (~c1_1(a2252)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(160,plain,
% 1.15/1.33 (((~c1_1(a2252)) | (~hskp58)) <=> ((~hskp58) | (~c1_1(a2252)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(161,axiom,((~c1_1(a2252)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.15/1.33 tff(162,plain,
% 1.15/1.33 ((~hskp58) | (~c1_1(a2252))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.15/1.33 tff(163,plain,
% 1.15/1.33 ((~hskp58) | (~c1_1(a2252))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[162, 159])).
% 1.15/1.33 tff(164,plain,
% 1.15/1.33 (~c1_1(a2252)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[163, 158])).
% 1.15/1.33 tff(165,plain,
% 1.15/1.33 (((~hskp58) | (~c2_1(a2252))) <=> ((~hskp58) | (~c2_1(a2252)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(166,plain,
% 1.15/1.33 (((~c2_1(a2252)) | (~hskp58)) <=> ((~hskp58) | (~c2_1(a2252)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(167,axiom,((~c2_1(a2252)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.15/1.33 tff(168,plain,
% 1.15/1.33 ((~hskp58) | (~c2_1(a2252))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.15/1.33 tff(169,plain,
% 1.15/1.33 ((~hskp58) | (~c2_1(a2252))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[168, 165])).
% 1.15/1.33 tff(170,plain,
% 1.15/1.33 (~c2_1(a2252)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[169, 158])).
% 1.15/1.33 tff(171,plain,
% 1.15/1.33 (((~hskp58) | c0_1(a2252)) <=> ((~hskp58) | c0_1(a2252))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(172,axiom,((~hskp58) | c0_1(a2252)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.15/1.33 tff(173,plain,
% 1.15/1.33 ((~hskp58) | c0_1(a2252)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.15/1.33 tff(174,plain,
% 1.15/1.33 ((~hskp58) | c0_1(a2252)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[173, 171])).
% 1.15/1.33 tff(175,plain,
% 1.15/1.33 ((~hskp58) | c0_1(a2252)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[174, 171])).
% 1.15/1.33 tff(176,plain,
% 1.15/1.33 ((~hskp58) | c0_1(a2252)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[175, 171])).
% 1.15/1.33 tff(177,plain,
% 1.15/1.33 ((~hskp58) | c0_1(a2252)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[176, 171])).
% 1.15/1.33 tff(178,plain,
% 1.15/1.33 (c0_1(a2252)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[177, 158])).
% 1.15/1.33 tff(179,plain,
% 1.15/1.33 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(180,plain,
% 1.15/1.33 ((hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(181,plain,
% 1.15/1.33 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[180])).
% 1.15/1.33 tff(182,plain,
% 1.15/1.33 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252)))),
% 1.15/1.33 inference(transitivity,[status(thm)],[181, 179])).
% 1.15/1.33 tff(183,plain,
% 1.15/1.33 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(184,plain,
% 1.15/1.33 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2252))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.15/1.33 tff(185,plain,
% 1.15/1.33 ($false),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[184, 150, 100, 178, 170, 164, 98, 97, 111, 101])).
% 1.15/1.33 tff(186,plain,((~c3_1(a2181)) | hskp32 | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.33 tff(187,plain,
% 1.15/1.33 (~c3_1(a2181)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[186, 100, 98, 97])).
% 1.15/1.33 tff(188,plain,
% 1.15/1.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(189,plain,
% 1.15/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[188])).
% 1.15/1.33 tff(190,plain,
% 1.15/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(191,plain,
% 1.15/1.33 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(192,plain,
% 1.15/1.33 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[191])).
% 1.15/1.33 tff(193,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause286')).
% 1.15/1.33 tff(194,plain,
% 1.15/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.15/1.33 tff(195,plain,
% 1.15/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.15/1.33 tff(196,plain,(
% 1.15/1.33 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 1.15/1.33 inference(skolemize,[status(sab)],[195])).
% 1.15/1.33 tff(197,plain,
% 1.15/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.15/1.33 tff(198,plain,
% 1.15/1.33 (^[U: $i] : refl((hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) <=> (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(199,plain,
% 1.15/1.33 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) <=> ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[198])).
% 1.15/1.33 tff(200,plain,
% 1.15/1.33 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) <=> ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(201,plain,
% 1.15/1.33 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U))), ((((~ndr1_0) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U)))), (((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U)) | c0_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))), (((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)))), ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp32))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp32) <=> (hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))), ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) <=> (hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)))), (((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2) <=> ((hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp32 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U)) | hskp2) <=> (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))), (((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2) <=> (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(202,plain,
% 1.15/1.33 (![U: $i] : ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2) <=> ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[201])).
% 1.15/1.33 tff(203,axiom,(![U: $i] : ((((((~ndr1_0) | c3_1(U)) | c1_1(U)) | c0_1(U)) | hskp32) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause243')).
% 1.15/1.33 tff(204,plain,
% 1.15/1.33 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.15/1.33 tff(205,plain,
% 1.15/1.33 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[204, 200])).
% 1.15/1.33 tff(206,plain,(
% 1.15/1.33 ![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 1.15/1.33 inference(skolemize,[status(sab)],[205])).
% 1.15/1.33 tff(207,plain,
% 1.15/1.33 (![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[206, 199])).
% 1.15/1.33 tff(208,plain,
% 1.15/1.33 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(209,plain,
% 1.15/1.33 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181)) <=> (hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(210,plain,
% 1.15/1.33 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181)))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[209])).
% 1.15/1.33 tff(211,plain,
% 1.15/1.33 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.15/1.33 inference(transitivity,[status(thm)],[210, 208])).
% 1.15/1.33 tff(212,plain,
% 1.15/1.33 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | c0_1(a2181))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(213,plain,
% 1.15/1.33 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2181) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.15/1.33 tff(214,plain,
% 1.15/1.33 (hskp32 | hskp2 | c0_1(a2181) | c3_1(a2181)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[213, 150, 98, 207])).
% 1.15/1.33 tff(215,plain,
% 1.15/1.33 (hskp2),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[214, 187, 99, 100])).
% 1.15/1.33 tff(216,plain,
% 1.15/1.33 (((~hskp2) | (~c2_1(a2187))) <=> ((~hskp2) | (~c2_1(a2187)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(217,plain,
% 1.15/1.33 (((~c2_1(a2187)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a2187)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(218,axiom,((~c2_1(a2187)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause236')).
% 1.15/1.33 tff(219,plain,
% 1.15/1.33 ((~hskp2) | (~c2_1(a2187))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[218, 217])).
% 1.15/1.33 tff(220,plain,
% 1.15/1.33 ((~hskp2) | (~c2_1(a2187))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[219, 216])).
% 1.15/1.33 tff(221,plain,
% 1.15/1.33 (~c2_1(a2187)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[220, 215])).
% 1.15/1.33 tff(222,plain,
% 1.15/1.33 (((~hskp2) | c3_1(a2187)) <=> ((~hskp2) | c3_1(a2187))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(223,axiom,((~hskp2) | c3_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.15/1.33 tff(224,plain,
% 1.15/1.33 ((~hskp2) | c3_1(a2187)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[223, 222])).
% 1.15/1.33 tff(225,plain,
% 1.15/1.33 ((~hskp2) | c3_1(a2187)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[224, 222])).
% 1.15/1.33 tff(226,plain,
% 1.15/1.33 ((~hskp2) | c3_1(a2187)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[225, 222])).
% 1.15/1.33 tff(227,plain,
% 1.15/1.33 ((~hskp2) | c3_1(a2187)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[226, 222])).
% 1.15/1.33 tff(228,plain,
% 1.15/1.33 ((~hskp2) | c3_1(a2187)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[227, 222])).
% 1.15/1.33 tff(229,plain,
% 1.15/1.33 (c3_1(a2187)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[228, 215])).
% 1.15/1.33 tff(230,plain,
% 1.15/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(231,plain,
% 1.15/1.33 (((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181)) <=> (c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(232,plain,
% 1.15/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[231])).
% 1.15/1.33 tff(233,plain,
% 1.15/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 1.15/1.33 inference(transitivity,[status(thm)],[232, 230])).
% 1.15/1.33 tff(234,plain,
% 1.15/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2181) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181) | c3_1(a2181) | c1_1(a2181))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(235,plain,
% 1.15/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2187) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | (~c0_1(a2187))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.15/1.33 tff(236,plain,
% 1.15/1.33 (~c0_1(a2187)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[235, 150, 229, 221, 99, 98, 97, 197, 187])).
% 1.15/1.33 tff(237,plain,
% 1.15/1.33 (^[V: $i, U: $i] : refl((hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(238,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[237])).
% 1.15/1.33 tff(239,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(240,plain,
% 1.15/1.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp33))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp33) <=> (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33) <=> (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(241,plain,
% 1.15/1.33 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33) <=> ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[240])).
% 1.15/1.33 tff(242,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c0_1(U)) | c1_1(V)) | c3_1(V)) | hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause269')).
% 1.15/1.33 tff(243,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[242, 241])).
% 1.15/1.33 tff(244,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[243, 239])).
% 1.15/1.33 tff(245,plain,(
% 1.15/1.33 ![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(skolemize,[status(sab)],[244])).
% 1.15/1.33 tff(246,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[245, 238])).
% 1.15/1.33 tff(247,plain,
% 1.15/1.33 (^[V: $i, U: $i] : refl((hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))),
% 1.15/1.33 inference(bind,[status(th)],[])).
% 1.15/1.33 tff(248,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.33 inference(quant_intro,[status(thm)],[247])).
% 1.15/1.33 tff(249,plain,
% 1.15/1.33 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(250,plain,
% 1.15/1.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp47))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp47) <=> (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47) <=> (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(251,plain,
% 1.15/1.34 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47) <=> ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[250])).
% 1.15/1.34 tff(252,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause264')).
% 1.15/1.34 tff(253,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[252, 251])).
% 1.15/1.34 tff(254,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[253, 249])).
% 1.15/1.34 tff(255,plain,(
% 1.15/1.34 ![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.34 inference(skolemize,[status(sab)],[254])).
% 1.15/1.34 tff(256,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[255, 248])).
% 1.15/1.34 tff(257,plain,
% 1.15/1.34 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(258,plain,
% 1.15/1.34 ((hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181)) <=> (hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(259,plain,
% 1.15/1.34 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187)))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[258])).
% 1.15/1.34 tff(260,plain,
% 1.15/1.34 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187))),
% 1.15/1.34 inference(transitivity,[status(thm)],[259, 257])).
% 1.15/1.34 tff(261,plain,
% 1.15/1.34 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(262,plain,
% 1.15/1.34 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2187) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | (~c3_1(a2187)) | c0_1(a2187)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[261, 260])).
% 1.15/1.34 tff(263,plain,
% 1.15/1.34 (hskp47),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[262, 150, 229, 221, 98, 97, 256, 187, 236])).
% 1.15/1.34 tff(264,plain,
% 1.15/1.34 (((~hskp47) | (~c1_1(a2226))) <=> ((~hskp47) | (~c1_1(a2226)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(265,plain,
% 1.15/1.34 (((~c1_1(a2226)) | (~hskp47)) <=> ((~hskp47) | (~c1_1(a2226)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(266,axiom,((~c1_1(a2226)) | (~hskp47)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.15/1.34 tff(267,plain,
% 1.15/1.34 ((~hskp47) | (~c1_1(a2226))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[266, 265])).
% 1.15/1.34 tff(268,plain,
% 1.15/1.34 ((~hskp47) | (~c1_1(a2226))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[267, 264])).
% 1.15/1.34 tff(269,plain,
% 1.15/1.34 (~c1_1(a2226)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[268, 263])).
% 1.15/1.34 tff(270,plain,
% 1.15/1.34 (((~hskp2) | c1_1(a2187)) <=> ((~hskp2) | c1_1(a2187))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(271,axiom,((~hskp2) | c1_1(a2187)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.15/1.34 tff(272,plain,
% 1.15/1.34 ((~hskp2) | c1_1(a2187)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.15/1.34 tff(273,plain,
% 1.15/1.34 ((~hskp2) | c1_1(a2187)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[272, 270])).
% 1.15/1.34 tff(274,plain,
% 1.15/1.34 ((~hskp2) | c1_1(a2187)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[273, 270])).
% 1.15/1.34 tff(275,plain,
% 1.15/1.34 ((~hskp2) | c1_1(a2187)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[274, 270])).
% 1.15/1.34 tff(276,plain,
% 1.15/1.34 ((~hskp2) | c1_1(a2187)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[275, 270])).
% 1.15/1.34 tff(277,plain,
% 1.15/1.34 (c1_1(a2187)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[276, 215])).
% 1.15/1.34 tff(278,plain,
% 1.15/1.34 (((~hskp47) | c0_1(a2226)) <=> ((~hskp47) | c0_1(a2226))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(279,axiom,((~hskp47) | c0_1(a2226)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.15/1.34 tff(280,plain,
% 1.15/1.34 ((~hskp47) | c0_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[279, 278])).
% 1.15/1.34 tff(281,plain,
% 1.15/1.34 ((~hskp47) | c0_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[280, 278])).
% 1.15/1.34 tff(282,plain,
% 1.15/1.34 ((~hskp47) | c0_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[281, 278])).
% 1.15/1.34 tff(283,plain,
% 1.15/1.34 ((~hskp47) | c0_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[282, 278])).
% 1.15/1.34 tff(284,plain,
% 1.15/1.34 ((~hskp47) | c0_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[283, 278])).
% 1.15/1.34 tff(285,plain,
% 1.15/1.34 (c0_1(a2226)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[284, 263])).
% 1.15/1.34 tff(286,plain,
% 1.15/1.34 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(287,plain,
% 1.15/1.34 ((hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226))) <=> (hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(288,plain,
% 1.15/1.34 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[287])).
% 1.15/1.34 tff(289,plain,
% 1.15/1.34 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226)))),
% 1.15/1.34 inference(transitivity,[status(thm)],[288, 286])).
% 1.15/1.34 tff(290,plain,
% 1.15/1.34 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c1_1(a2187)) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(291,plain,
% 1.15/1.34 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2226) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | c0_1(a2187) | c3_1(a2226) | (~c0_1(a2226))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.15/1.34 tff(292,plain,
% 1.15/1.34 (c3_1(a2226)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[291, 150, 72, 285, 277, 269, 221, 246, 236])).
% 1.15/1.34 tff(293,plain,
% 1.15/1.34 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(294,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[293])).
% 1.15/1.34 tff(295,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(296,plain,
% 1.15/1.34 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) <=> (((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c2_1(W) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(297,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[296])).
% 1.15/1.34 tff(298,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c0_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c2_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause295')).
% 1.15/1.34 tff(299,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.15/1.34 tff(300,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[299, 295])).
% 1.15/1.34 tff(301,plain,(
% 1.15/1.34 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.34 inference(skolemize,[status(sab)],[300])).
% 1.15/1.34 tff(302,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[301, 294])).
% 1.15/1.34 tff(303,plain,
% 1.15/1.34 (((~hskp47) | c2_1(a2226)) <=> ((~hskp47) | c2_1(a2226))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(304,axiom,((~hskp47) | c2_1(a2226)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.15/1.34 tff(305,plain,
% 1.15/1.34 ((~hskp47) | c2_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[304, 303])).
% 1.15/1.34 tff(306,plain,
% 1.15/1.34 ((~hskp47) | c2_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[305, 303])).
% 1.15/1.34 tff(307,plain,
% 1.15/1.34 ((~hskp47) | c2_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[306, 303])).
% 1.15/1.34 tff(308,plain,
% 1.15/1.34 ((~hskp47) | c2_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[307, 303])).
% 1.15/1.34 tff(309,plain,
% 1.15/1.34 ((~hskp47) | c2_1(a2226)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[308, 303])).
% 1.15/1.34 tff(310,plain,
% 1.15/1.34 (c2_1(a2226)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[309, 263])).
% 1.15/1.34 tff(311,plain,
% 1.15/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(312,plain,
% 1.15/1.34 (((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187))) <=> (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(313,plain,
% 1.15/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[312])).
% 1.15/1.34 tff(314,plain,
% 1.15/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 1.15/1.34 inference(transitivity,[status(thm)],[313, 311])).
% 1.15/1.34 tff(315,plain,
% 1.15/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2226)) | (~c0_1(a2226)) | (~c2_1(a2226)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(316,plain,
% 1.15/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c3_1(a2226)) | (~c2_1(a2226)) | (~c0_1(a2226))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[315, 314])).
% 1.15/1.34 tff(317,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[316, 150, 310, 285, 229, 277, 221, 302, 236, 292])).
% 1.15/1.34 tff(318,plain,(hskp32 | hskp33 | c1_1(a2181) | c2_1(a2181) | c0_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(319,plain,
% 1.15/1.34 (hskp32),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[318, 99, 98, 97, 72])).
% 1.15/1.34 tff(320,plain,
% 1.15/1.34 (((~hskp32) | (~c2_1(a2186))) <=> ((~hskp32) | (~c2_1(a2186)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(321,plain,
% 1.15/1.34 (((~c2_1(a2186)) | (~hskp32)) <=> ((~hskp32) | (~c2_1(a2186)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(322,axiom,((~c2_1(a2186)) | (~hskp32)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.15/1.34 tff(323,plain,
% 1.15/1.34 ((~hskp32) | (~c2_1(a2186))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.15/1.34 tff(324,plain,
% 1.15/1.34 ((~hskp32) | (~c2_1(a2186))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[323, 320])).
% 1.15/1.34 tff(325,plain,
% 1.15/1.34 (~c2_1(a2186)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[324, 319])).
% 1.15/1.34 tff(326,plain,
% 1.15/1.34 (~c3_1(a2186)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[86, 319])).
% 1.15/1.34 tff(327,plain,
% 1.15/1.34 (c0_1(a2186)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[80, 319])).
% 1.15/1.34 tff(328,assumption,(~hskp34), introduced(assumption)).
% 1.15/1.34 tff(329,assumption,(c1_1(a2186)), introduced(assumption)).
% 1.15/1.34 tff(330,plain,
% 1.15/1.34 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(331,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[330])).
% 1.15/1.34 tff(332,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(333,plain,
% 1.15/1.34 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c2_1(W) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(334,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[333])).
% 1.15/1.34 tff(335,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c2_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause293')).
% 1.15/1.34 tff(336,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[335, 334])).
% 1.15/1.34 tff(337,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[336, 332])).
% 1.15/1.34 tff(338,plain,(
% 1.15/1.34 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.34 inference(skolemize,[status(sab)],[337])).
% 1.15/1.34 tff(339,plain,
% 1.15/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[338, 331])).
% 1.15/1.34 tff(340,plain,
% 1.15/1.34 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(341,plain,
% 1.15/1.34 ((hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186))) <=> (hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(342,plain,
% 1.15/1.34 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[341])).
% 1.15/1.34 tff(343,plain,
% 1.15/1.34 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)))),
% 1.15/1.34 inference(transitivity,[status(thm)],[342, 340])).
% 1.15/1.34 tff(344,plain,
% 1.15/1.34 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(345,plain,
% 1.15/1.34 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.15/1.34 tff(346,plain,
% 1.15/1.34 (hskp18 | (~c1_1(a2186))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[345, 150, 326, 325, 61])).
% 1.15/1.34 tff(347,plain,
% 1.15/1.34 (hskp18),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[346, 329])).
% 1.15/1.34 tff(348,plain,
% 1.15/1.34 (((~hskp18) | (~c2_1(a2222))) <=> ((~hskp18) | (~c2_1(a2222)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(349,plain,
% 1.15/1.34 (((~c2_1(a2222)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2222)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(350,axiom,((~c2_1(a2222)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 1.15/1.34 tff(351,plain,
% 1.15/1.34 ((~hskp18) | (~c2_1(a2222))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.15/1.34 tff(352,plain,
% 1.15/1.34 ((~hskp18) | (~c2_1(a2222))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[351, 348])).
% 1.15/1.34 tff(353,plain,
% 1.15/1.34 (~c2_1(a2222)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[352, 347])).
% 1.15/1.34 tff(354,plain,
% 1.15/1.34 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) <=> (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(355,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[354])).
% 1.15/1.34 tff(356,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(357,plain,
% 1.15/1.34 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | hskp38))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38) <=> (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))))),
% 1.15/1.34 inference(bind,[status(th)],[])).
% 1.15/1.34 tff(358,plain,
% 1.15/1.34 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 1.15/1.34 inference(quant_intro,[status(thm)],[357])).
% 1.15/1.34 tff(359,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c0_1(U))) | c2_1(V)) | c1_1(V)) | c0_1(V)) | c3_1(U)) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause266')).
% 1.15/1.34 tff(360,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[359, 358])).
% 1.15/1.34 tff(361,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[360, 356])).
% 1.15/1.34 tff(362,plain,(
% 1.15/1.34 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 1.15/1.34 inference(skolemize,[status(sab)],[361])).
% 1.15/1.34 tff(363,plain,
% 1.15/1.34 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[362, 355])).
% 1.15/1.34 tff(364,plain,
% 1.15/1.34 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(365,plain,
% 1.15/1.35 ((hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)) <=> (hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(366,plain,
% 1.15/1.35 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[365])).
% 1.15/1.35 tff(367,plain,
% 1.15/1.35 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[366, 364])).
% 1.15/1.35 tff(368,plain,
% 1.15/1.35 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2186)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(369,plain,
% 1.15/1.35 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2186)) | (~c0_1(a2186))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.15/1.35 tff(370,plain,
% 1.15/1.35 (hskp38 | (~c1_1(a2186))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[369, 150, 327, 326, 99, 98, 97, 363])).
% 1.15/1.35 tff(371,plain,
% 1.15/1.35 (hskp38),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[370, 329])).
% 1.15/1.35 tff(372,plain,
% 1.15/1.35 (((~hskp38) | (~c2_1(a2200))) <=> ((~hskp38) | (~c2_1(a2200)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(373,plain,
% 1.15/1.35 (((~c2_1(a2200)) | (~hskp38)) <=> ((~hskp38) | (~c2_1(a2200)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(374,axiom,((~c2_1(a2200)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.15/1.35 tff(375,plain,
% 1.15/1.35 ((~hskp38) | (~c2_1(a2200))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[374, 373])).
% 1.15/1.35 tff(376,plain,
% 1.15/1.35 ((~hskp38) | (~c2_1(a2200))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[375, 372])).
% 1.15/1.35 tff(377,plain,
% 1.15/1.35 (~c2_1(a2200)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[376, 371])).
% 1.15/1.35 tff(378,plain,
% 1.15/1.35 (((~hskp38) | (~c0_1(a2200))) <=> ((~hskp38) | (~c0_1(a2200)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(379,plain,
% 1.15/1.35 (((~c0_1(a2200)) | (~hskp38)) <=> ((~hskp38) | (~c0_1(a2200)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(380,axiom,((~c0_1(a2200)) | (~hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.15/1.35 tff(381,plain,
% 1.15/1.35 ((~hskp38) | (~c0_1(a2200))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[380, 379])).
% 1.15/1.35 tff(382,plain,
% 1.15/1.35 ((~hskp38) | (~c0_1(a2200))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[381, 378])).
% 1.15/1.35 tff(383,plain,
% 1.15/1.35 (~c0_1(a2200)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[382, 371])).
% 1.15/1.35 tff(384,plain,
% 1.15/1.35 (((~hskp18) | c3_1(a2222)) <=> ((~hskp18) | c3_1(a2222))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(385,axiom,((~hskp18) | c3_1(a2222)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 1.15/1.35 tff(386,plain,
% 1.15/1.35 ((~hskp18) | c3_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.15/1.35 tff(387,plain,
% 1.15/1.35 ((~hskp18) | c3_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[386, 384])).
% 1.15/1.35 tff(388,plain,
% 1.15/1.35 ((~hskp18) | c3_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[387, 384])).
% 1.15/1.35 tff(389,plain,
% 1.15/1.35 ((~hskp18) | c3_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[388, 384])).
% 1.15/1.35 tff(390,plain,
% 1.15/1.35 ((~hskp18) | c3_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[389, 384])).
% 1.15/1.35 tff(391,plain,
% 1.15/1.35 (c3_1(a2222)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[390, 347])).
% 1.15/1.35 tff(392,plain,
% 1.15/1.35 (((~hskp38) | c1_1(a2200)) <=> ((~hskp38) | c1_1(a2200))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(393,axiom,((~hskp38) | c1_1(a2200)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.15/1.35 tff(394,plain,
% 1.15/1.35 ((~hskp38) | c1_1(a2200)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[393, 392])).
% 1.15/1.35 tff(395,plain,
% 1.15/1.35 ((~hskp38) | c1_1(a2200)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[394, 392])).
% 1.15/1.35 tff(396,plain,
% 1.15/1.35 ((~hskp38) | c1_1(a2200)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[395, 392])).
% 1.15/1.35 tff(397,plain,
% 1.15/1.35 ((~hskp38) | c1_1(a2200)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[396, 392])).
% 1.15/1.35 tff(398,plain,
% 1.15/1.35 ((~hskp38) | c1_1(a2200)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[397, 392])).
% 1.15/1.35 tff(399,plain,
% 1.15/1.35 (c1_1(a2200)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[398, 371])).
% 1.15/1.35 tff(400,plain,
% 1.15/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(401,plain,
% 1.15/1.35 (((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200))) <=> (c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(402,plain,
% 1.15/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[401])).
% 1.15/1.35 tff(403,plain,
% 1.15/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[402, 400])).
% 1.15/1.35 tff(404,plain,
% 1.15/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(405,plain,
% 1.15/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c1_1(a2186)) | (~c0_1(a2186)) | (~c1_1(a2200))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[404, 403])).
% 1.15/1.35 tff(406,plain,
% 1.15/1.35 (~c1_1(a2222)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[405, 150, 399, 327, 391, 383, 377, 325, 353, 339, 329])).
% 1.15/1.35 tff(407,plain,
% 1.15/1.35 (^[U: $i] : refl((hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(408,plain,
% 1.15/1.35 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[407])).
% 1.15/1.35 tff(409,plain,
% 1.15/1.35 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(410,plain,
% 1.15/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp46))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp46) <=> (hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) <=> (hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34) <=> ((hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp34))), rewrite(((hskp46 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp34) <=> (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34) <=> (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(411,plain,
% 1.15/1.35 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34) <=> ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[410])).
% 1.15/1.35 tff(412,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp46) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause259')).
% 1.15/1.35 tff(413,plain,
% 1.15/1.35 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.15/1.35 tff(414,plain,
% 1.15/1.35 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[413, 409])).
% 1.15/1.35 tff(415,plain,(
% 1.15/1.35 ![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.35 inference(skolemize,[status(sab)],[414])).
% 1.15/1.35 tff(416,plain,
% 1.15/1.35 (![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[415, 408])).
% 1.15/1.35 tff(417,plain,
% 1.15/1.35 (((~hskp18) | c0_1(a2222)) <=> ((~hskp18) | c0_1(a2222))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(418,axiom,((~hskp18) | c0_1(a2222)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.15/1.35 tff(419,plain,
% 1.15/1.35 ((~hskp18) | c0_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.15/1.35 tff(420,plain,
% 1.15/1.35 ((~hskp18) | c0_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[419, 417])).
% 1.15/1.35 tff(421,plain,
% 1.15/1.35 ((~hskp18) | c0_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[420, 417])).
% 1.15/1.35 tff(422,plain,
% 1.15/1.35 ((~hskp18) | c0_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[421, 417])).
% 1.15/1.35 tff(423,plain,
% 1.15/1.35 ((~hskp18) | c0_1(a2222)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[422, 417])).
% 1.15/1.35 tff(424,plain,
% 1.15/1.35 (c0_1(a2222)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[423, 347])).
% 1.15/1.35 tff(425,plain,
% 1.15/1.35 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(426,plain,
% 1.15/1.35 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(427,plain,
% 1.15/1.35 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[426, 425])).
% 1.15/1.35 tff(428,plain,
% 1.15/1.35 (hskp46 | c1_1(a2222)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[427, 150, 328, 424, 391, 416])).
% 1.15/1.35 tff(429,plain,
% 1.15/1.35 (hskp46),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[428, 406])).
% 1.15/1.35 tff(430,plain,
% 1.15/1.35 (((~hskp46) | c2_1(a2218)) <=> ((~hskp46) | c2_1(a2218))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(431,axiom,((~hskp46) | c2_1(a2218)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.15/1.35 tff(432,plain,
% 1.15/1.35 ((~hskp46) | c2_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.15/1.35 tff(433,plain,
% 1.15/1.35 ((~hskp46) | c2_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[432, 430])).
% 1.15/1.35 tff(434,plain,
% 1.15/1.35 ((~hskp46) | c2_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[433, 430])).
% 1.15/1.35 tff(435,plain,
% 1.15/1.35 ((~hskp46) | c2_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[434, 430])).
% 1.15/1.35 tff(436,plain,
% 1.15/1.35 ((~hskp46) | c2_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[435, 430])).
% 1.15/1.35 tff(437,plain,
% 1.15/1.35 (c2_1(a2218)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[436, 429])).
% 1.15/1.35 tff(438,plain,
% 1.15/1.35 (((~hskp46) | c0_1(a2218)) <=> ((~hskp46) | c0_1(a2218))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(439,axiom,((~hskp46) | c0_1(a2218)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.15/1.35 tff(440,plain,
% 1.15/1.35 ((~hskp46) | c0_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.15/1.35 tff(441,plain,
% 1.15/1.35 ((~hskp46) | c0_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[440, 438])).
% 1.15/1.35 tff(442,plain,
% 1.15/1.35 ((~hskp46) | c0_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[441, 438])).
% 1.15/1.35 tff(443,plain,
% 1.15/1.35 ((~hskp46) | c0_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[442, 438])).
% 1.15/1.35 tff(444,plain,
% 1.15/1.35 ((~hskp46) | c0_1(a2218)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[443, 438])).
% 1.15/1.35 tff(445,plain,
% 1.15/1.35 (c0_1(a2218)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[444, 429])).
% 1.15/1.35 tff(446,plain,
% 1.15/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(447,plain,
% 1.15/1.35 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(448,plain,
% 1.15/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[447])).
% 1.15/1.35 tff(449,plain,
% 1.15/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[448, 446])).
% 1.15/1.35 tff(450,plain,
% 1.15/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2222) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(451,plain,
% 1.15/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[450, 449])).
% 1.15/1.35 tff(452,plain,
% 1.15/1.35 (~c1_1(a2218)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[451, 150, 445, 437, 327, 391, 326, 325, 353, 51, 406])).
% 1.15/1.35 tff(453,plain,
% 1.15/1.35 (^[U: $i] : refl((hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(454,plain,
% 1.15/1.35 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[453])).
% 1.15/1.35 tff(455,plain,
% 1.15/1.35 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(456,plain,
% 1.15/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp33))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp33) <=> (hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) <=> (hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34) <=> ((hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp34))), rewrite(((hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp34) <=> (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34) <=> (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(457,plain,
% 1.15/1.35 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34) <=> ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[456])).
% 1.15/1.35 tff(458,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp33) | hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause257')).
% 1.15/1.35 tff(459,plain,
% 1.15/1.35 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.15/1.35 tff(460,plain,
% 1.15/1.35 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[459, 455])).
% 1.15/1.35 tff(461,plain,(
% 1.15/1.35 ![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.15/1.35 inference(skolemize,[status(sab)],[460])).
% 1.15/1.35 tff(462,plain,
% 1.15/1.35 (![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[461, 454])).
% 1.15/1.35 tff(463,plain,
% 1.15/1.35 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(464,plain,
% 1.15/1.35 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(465,plain,
% 1.15/1.35 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[464, 463])).
% 1.15/1.35 tff(466,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[465, 150, 328, 72, 445, 437, 462, 452])).
% 1.15/1.35 tff(467,plain,((~c1_1(a2186)) | hskp34 | hskp33 | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(468,plain,
% 1.15/1.35 (~c1_1(a2186)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[467, 328, 72, 99, 98, 97])).
% 1.15/1.35 tff(469,assumption,(~c1_1(a2186)), introduced(assumption)).
% 1.15/1.35 tff(470,plain,
% 1.15/1.35 (^[V: $i, U: $i] : refl((hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(471,plain,
% 1.15/1.35 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[470])).
% 1.15/1.35 tff(472,plain,
% 1.15/1.35 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(473,plain,
% 1.15/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(V))), (((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V))), (((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c3_1(V) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp53))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(474,plain,
% 1.15/1.35 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53) <=> ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[473])).
% 1.15/1.35 tff(475,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c0_1(U))) | c3_1(V)) | c2_1(V)) | c1_1(V)) | c3_1(U)) | c1_1(U)) | hskp53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause265')).
% 1.15/1.35 tff(476,plain,
% 1.15/1.35 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.15/1.35 tff(477,plain,
% 1.15/1.35 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[476, 472])).
% 1.15/1.35 tff(478,plain,(
% 1.15/1.35 ![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.35 inference(skolemize,[status(sab)],[477])).
% 1.15/1.35 tff(479,plain,
% 1.15/1.35 (![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[478, 471])).
% 1.15/1.35 tff(480,assumption,(~c2_1(a2186)), introduced(assumption)).
% 1.15/1.35 tff(481,assumption,(~c3_1(a2186)), introduced(assumption)).
% 1.15/1.35 tff(482,assumption,(c0_1(a2186)), introduced(assumption)).
% 1.15/1.35 tff(483,assumption,(~hskp53), introduced(assumption)).
% 1.15/1.35 tff(484,plain,
% 1.15/1.35 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(485,plain,
% 1.15/1.35 ((hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186)) <=> (hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(486,plain,
% 1.15/1.35 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[485])).
% 1.15/1.35 tff(487,plain,
% 1.15/1.35 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[486, 484])).
% 1.15/1.35 tff(488,plain,
% 1.15/1.35 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2186) | c3_1(a2186) | c2_1(a2186))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(489,plain,
% 1.15/1.35 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[488, 487])).
% 1.15/1.35 tff(490,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[489, 150, 483, 482, 481, 480, 479, 469])).
% 1.15/1.35 tff(491,plain,(c1_1(a2186) | hskp53 | (~c0_1(a2186)) | c3_1(a2186) | c2_1(a2186)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(492,plain,
% 1.15/1.35 (hskp53),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[491, 468, 327, 326, 325])).
% 1.15/1.35 tff(493,plain,
% 1.15/1.35 (c0_1(a2235)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[95, 492])).
% 1.15/1.35 tff(494,assumption,(~hskp37), introduced(assumption)).
% 1.15/1.35 tff(495,plain,
% 1.15/1.35 (^[U: $i] : refl((hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(496,plain,
% 1.15/1.35 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[495])).
% 1.15/1.35 tff(497,plain,
% 1.15/1.35 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(498,plain,
% 1.15/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37) <=> ((hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp37))), rewrite(((hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp37) <=> (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37) <=> (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 1.15/1.35 inference(bind,[status(th)],[])).
% 1.15/1.35 tff(499,plain,
% 1.15/1.35 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37) <=> ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.15/1.35 inference(quant_intro,[status(thm)],[498])).
% 1.15/1.35 tff(500,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 1.15/1.35 tff(501,plain,
% 1.15/1.35 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[500, 499])).
% 1.15/1.35 tff(502,plain,
% 1.15/1.35 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[501, 497])).
% 1.15/1.35 tff(503,plain,(
% 1.15/1.35 ![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.15/1.35 inference(skolemize,[status(sab)],[502])).
% 1.15/1.35 tff(504,plain,
% 1.15/1.35 (![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[503, 496])).
% 1.15/1.35 tff(505,plain,
% 1.15/1.35 (((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))) <=> ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(506,plain,
% 1.15/1.35 ((hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(507,plain,
% 1.15/1.35 (((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[506])).
% 1.15/1.35 tff(508,plain,
% 1.15/1.35 (((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[507, 505])).
% 1.15/1.35 tff(509,plain,
% 1.15/1.35 ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp37 | hskp7 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(510,plain,
% 1.15/1.35 ((~![U: $i] : (hskp37 | hskp7 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp37 | hskp7 | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.15/1.35 tff(511,plain,
% 1.15/1.35 (hskp37 | hskp7),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[510, 150, 327, 326, 325, 504])).
% 1.15/1.35 tff(512,plain,
% 1.15/1.35 (hskp7),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[511, 494])).
% 1.15/1.35 tff(513,plain,
% 1.15/1.35 (((~hskp7) | c0_1(a2198)) <=> ((~hskp7) | c0_1(a2198))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(514,axiom,((~hskp7) | c0_1(a2198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.15/1.35 tff(515,plain,
% 1.15/1.35 ((~hskp7) | c0_1(a2198)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.15/1.35 tff(516,plain,
% 1.15/1.35 ((~hskp7) | c0_1(a2198)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[515, 513])).
% 1.15/1.35 tff(517,plain,
% 1.15/1.35 ((~hskp7) | c0_1(a2198)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[516, 513])).
% 1.15/1.36 tff(518,plain,
% 1.15/1.36 ((~hskp7) | c0_1(a2198)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[517, 513])).
% 1.15/1.36 tff(519,plain,
% 1.15/1.36 ((~hskp7) | c0_1(a2198)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[518, 513])).
% 1.15/1.36 tff(520,plain,
% 1.15/1.36 (c0_1(a2198)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[519, 512])).
% 1.15/1.36 tff(521,plain,
% 1.15/1.36 (((~hskp7) | c2_1(a2198)) <=> ((~hskp7) | c2_1(a2198))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(522,axiom,((~hskp7) | c2_1(a2198)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.15/1.36 tff(523,plain,
% 1.15/1.36 ((~hskp7) | c2_1(a2198)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[522, 521])).
% 1.15/1.36 tff(524,plain,
% 1.15/1.36 ((~hskp7) | c2_1(a2198)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[523, 521])).
% 1.15/1.36 tff(525,plain,
% 1.15/1.36 ((~hskp7) | c2_1(a2198)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[524, 521])).
% 1.15/1.36 tff(526,plain,
% 1.15/1.36 ((~hskp7) | c2_1(a2198)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[525, 521])).
% 1.15/1.36 tff(527,plain,
% 1.15/1.36 ((~hskp7) | c2_1(a2198)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[526, 521])).
% 1.15/1.36 tff(528,plain,
% 1.15/1.36 (c2_1(a2198)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[527, 512])).
% 1.15/1.36 tff(529,plain,
% 1.15/1.36 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(530,plain,
% 1.15/1.36 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(531,plain,
% 1.15/1.36 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[530, 529])).
% 1.15/1.36 tff(532,plain,
% 1.15/1.36 (c1_1(a2198)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[531, 150, 328, 72, 528, 520, 462])).
% 1.15/1.36 tff(533,plain,
% 1.15/1.36 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)))),
% 1.15/1.36 inference(bind,[status(th)],[])).
% 1.15/1.36 tff(534,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 1.15/1.36 inference(quant_intro,[status(thm)],[533])).
% 1.15/1.36 tff(535,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(536,plain,
% 1.15/1.36 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))))),
% 1.15/1.36 inference(bind,[status(th)],[])).
% 1.15/1.36 tff(537,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 1.15/1.36 inference(quant_intro,[status(thm)],[536])).
% 1.15/1.36 tff(538,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(W)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause287')).
% 1.15/1.36 tff(539,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[538, 537])).
% 1.15/1.36 tff(540,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[539, 535])).
% 1.15/1.36 tff(541,plain,(
% 1.15/1.36 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 1.15/1.36 inference(skolemize,[status(sab)],[540])).
% 1.15/1.36 tff(542,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[541, 534])).
% 1.15/1.36 tff(543,plain,
% 1.15/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(544,plain,
% 1.15/1.36 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181)) <=> (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(545,plain,
% 1.15/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[544])).
% 1.15/1.36 tff(546,plain,
% 1.15/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[545, 543])).
% 1.15/1.36 tff(547,plain,
% 1.15/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2198)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(548,plain,
% 1.15/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c1_1(a2186))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[547, 546])).
% 1.15/1.36 tff(549,plain,
% 1.15/1.36 (~c1_1(a2186)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[548, 150, 528, 520, 326, 325, 99, 98, 97, 542, 532])).
% 1.15/1.36 tff(550,plain,
% 1.15/1.36 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))))),
% 1.15/1.36 inference(bind,[status(th)],[])).
% 1.15/1.36 tff(551,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.15/1.36 inference(quant_intro,[status(thm)],[550])).
% 1.15/1.36 tff(552,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(553,plain,
% 1.15/1.36 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))))),
% 1.15/1.36 inference(bind,[status(th)],[])).
% 1.15/1.36 tff(554,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.15/1.36 inference(quant_intro,[status(thm)],[553])).
% 1.15/1.36 tff(555,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause291')).
% 1.15/1.36 tff(556,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.15/1.36 tff(557,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[556, 552])).
% 1.15/1.36 tff(558,plain,(
% 1.15/1.36 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.15/1.36 inference(skolemize,[status(sab)],[557])).
% 1.15/1.36 tff(559,plain,
% 1.15/1.36 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[558, 551])).
% 1.15/1.36 tff(560,plain,
% 1.15/1.36 ((hskp37 | hskp34 | hskp6) <=> (hskp37 | hskp34 | hskp6)),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(561,plain,
% 1.15/1.36 (((hskp34 | hskp37) | hskp6) <=> (hskp37 | hskp34 | hskp6)),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(562,axiom,((hskp34 | hskp37) | hskp6), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.15/1.36 tff(563,plain,
% 1.15/1.36 (hskp37 | hskp34 | hskp6),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.15/1.36 tff(564,plain,
% 1.15/1.36 (hskp37 | hskp34 | hskp6),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[563, 560])).
% 1.15/1.36 tff(565,plain,
% 1.15/1.36 (hskp37 | hskp34 | hskp6),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[564, 560])).
% 1.15/1.36 tff(566,plain,
% 1.15/1.36 (hskp37 | hskp34 | hskp6),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[565, 560])).
% 1.15/1.36 tff(567,plain,
% 1.15/1.36 (hskp37 | hskp34 | hskp6),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[566, 560])).
% 1.15/1.36 tff(568,plain,
% 1.15/1.36 (hskp6),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[567, 494, 328])).
% 1.15/1.36 tff(569,plain,
% 1.15/1.36 (((~hskp6) | (~c1_1(a2197))) <=> ((~hskp6) | (~c1_1(a2197)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(570,plain,
% 1.15/1.36 (((~c1_1(a2197)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a2197)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(571,axiom,((~c1_1(a2197)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause229')).
% 1.15/1.36 tff(572,plain,
% 1.15/1.36 ((~hskp6) | (~c1_1(a2197))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.15/1.36 tff(573,plain,
% 1.15/1.36 ((~hskp6) | (~c1_1(a2197))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[572, 569])).
% 1.15/1.36 tff(574,plain,
% 1.15/1.36 (~c1_1(a2197)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[573, 568])).
% 1.15/1.36 tff(575,plain,
% 1.15/1.36 (((~hskp6) | (~c0_1(a2197))) <=> ((~hskp6) | (~c0_1(a2197)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(576,plain,
% 1.15/1.36 (((~c0_1(a2197)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a2197)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(577,axiom,((~c0_1(a2197)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause227')).
% 1.15/1.36 tff(578,plain,
% 1.15/1.36 ((~hskp6) | (~c0_1(a2197))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.15/1.36 tff(579,plain,
% 1.15/1.36 ((~hskp6) | (~c0_1(a2197))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[578, 575])).
% 1.15/1.36 tff(580,plain,
% 1.15/1.36 (~c0_1(a2197)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[579, 568])).
% 1.15/1.36 tff(581,plain,
% 1.15/1.36 (((~hskp7) | (~c3_1(a2198))) <=> ((~hskp7) | (~c3_1(a2198)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(582,plain,
% 1.15/1.36 (((~c3_1(a2198)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a2198)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(583,axiom,((~c3_1(a2198)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause226')).
% 1.15/1.36 tff(584,plain,
% 1.15/1.36 ((~hskp7) | (~c3_1(a2198))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.15/1.36 tff(585,plain,
% 1.15/1.36 ((~hskp7) | (~c3_1(a2198))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[584, 581])).
% 1.15/1.36 tff(586,plain,
% 1.15/1.36 (~c3_1(a2198)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[585, 512])).
% 1.15/1.36 tff(587,plain,
% 1.15/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(588,plain,
% 1.15/1.36 (((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(589,plain,
% 1.15/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[588])).
% 1.15/1.36 tff(590,plain,
% 1.15/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[589, 587])).
% 1.15/1.36 tff(591,plain,
% 1.15/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(592,plain,
% 1.15/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2186) | c2_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | (~c0_1(a2186))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[591, 590])).
% 1.15/1.36 tff(593,plain,
% 1.15/1.36 (~c2_1(a2197)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[592, 150, 327, 528, 520, 326, 325, 586, 580, 574, 559])).
% 1.15/1.36 tff(594,plain,
% 1.15/1.36 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(595,plain,
% 1.15/1.36 ((hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197)) <=> (hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(596,plain,
% 1.15/1.36 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[595])).
% 1.15/1.36 tff(597,plain,
% 1.15/1.36 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[596, 594])).
% 1.15/1.36 tff(598,plain,
% 1.15/1.36 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2197) | c1_1(a2197) | c2_1(a2197))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(599,plain,
% 1.15/1.36 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c1_1(a2198)) | (~c0_1(a2198))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.15/1.36 tff(600,plain,
% 1.15/1.36 (hskp38),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[599, 150, 520, 586, 580, 574, 363, 532, 593])).
% 1.15/1.36 tff(601,plain,
% 1.15/1.36 (~c2_1(a2200)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[376, 600])).
% 1.15/1.36 tff(602,plain,
% 1.15/1.36 (~c0_1(a2200)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[382, 600])).
% 1.15/1.36 tff(603,plain,
% 1.15/1.36 (c1_1(a2200)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[398, 600])).
% 1.15/1.36 tff(604,plain,
% 1.15/1.36 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(605,plain,
% 1.15/1.36 ((hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(606,plain,
% 1.15/1.36 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[605])).
% 1.15/1.36 tff(607,plain,
% 1.15/1.36 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[606, 604])).
% 1.15/1.36 tff(608,plain,
% 1.15/1.36 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c1_1(a2200)) | c1_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(609,plain,
% 1.15/1.36 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2200) | c2_1(a2200) | c3_1(a2186) | (~ndr1_0) | c1_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2200))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.15/1.36 tff(610,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[609, 150, 72, 603, 327, 602, 601, 326, 246, 549])).
% 1.15/1.36 tff(611,plain,(hskp37 | hskp33 | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | hskp34), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(612,plain,
% 1.15/1.36 (hskp37),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[611, 328, 99, 98, 97, 72])).
% 1.15/1.36 tff(613,plain,
% 1.15/1.36 (((~hskp53) | c2_1(a2235)) <=> ((~hskp53) | c2_1(a2235))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(614,axiom,((~hskp53) | c2_1(a2235)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.15/1.36 tff(615,plain,
% 1.15/1.36 ((~hskp53) | c2_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.15/1.36 tff(616,plain,
% 1.15/1.36 ((~hskp53) | c2_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[615, 613])).
% 1.15/1.36 tff(617,plain,
% 1.15/1.36 ((~hskp53) | c2_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[616, 613])).
% 1.15/1.36 tff(618,plain,
% 1.15/1.36 ((~hskp53) | c2_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[617, 613])).
% 1.15/1.36 tff(619,plain,
% 1.15/1.36 ((~hskp53) | c2_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[618, 613])).
% 1.15/1.36 tff(620,plain,
% 1.15/1.36 (c2_1(a2235)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[619, 492])).
% 1.15/1.36 tff(621,plain,
% 1.15/1.36 (((~hskp53) | c3_1(a2235)) <=> ((~hskp53) | c3_1(a2235))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(622,axiom,((~hskp53) | c3_1(a2235)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.15/1.36 tff(623,plain,
% 1.15/1.36 ((~hskp53) | c3_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[622, 621])).
% 1.15/1.36 tff(624,plain,
% 1.15/1.36 ((~hskp53) | c3_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[623, 621])).
% 1.15/1.36 tff(625,plain,
% 1.15/1.36 ((~hskp53) | c3_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[624, 621])).
% 1.15/1.36 tff(626,plain,
% 1.15/1.36 ((~hskp53) | c3_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[625, 621])).
% 1.15/1.36 tff(627,plain,
% 1.15/1.36 ((~hskp53) | c3_1(a2235)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[626, 621])).
% 1.15/1.36 tff(628,plain,
% 1.15/1.36 (c3_1(a2235)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[627, 492])).
% 1.15/1.36 tff(629,assumption,(hskp37), introduced(assumption)).
% 1.15/1.36 tff(630,plain,
% 1.15/1.36 (((~hskp37) | (~c0_1(a2196))) <=> ((~hskp37) | (~c0_1(a2196)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(631,plain,
% 1.15/1.36 (((~c0_1(a2196)) | (~hskp37)) <=> ((~hskp37) | (~c0_1(a2196)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(632,axiom,((~c0_1(a2196)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.15/1.36 tff(633,plain,
% 1.15/1.36 ((~hskp37) | (~c0_1(a2196))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[632, 631])).
% 1.15/1.36 tff(634,plain,
% 1.15/1.36 ((~hskp37) | (~c0_1(a2196))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[633, 630])).
% 1.15/1.36 tff(635,plain,
% 1.15/1.36 (~c0_1(a2196)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[634, 629])).
% 1.15/1.36 tff(636,plain,
% 1.15/1.36 (((~hskp37) | c2_1(a2196)) <=> ((~hskp37) | c2_1(a2196))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(637,axiom,((~hskp37) | c2_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.15/1.36 tff(638,plain,
% 1.15/1.36 ((~hskp37) | c2_1(a2196)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[637, 636])).
% 1.15/1.36 tff(639,plain,
% 1.15/1.36 ((~hskp37) | c2_1(a2196)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[638, 636])).
% 1.15/1.36 tff(640,plain,
% 1.15/1.36 ((~hskp37) | c2_1(a2196)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[639, 636])).
% 1.15/1.36 tff(641,plain,
% 1.15/1.36 ((~hskp37) | c2_1(a2196)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[640, 636])).
% 1.15/1.36 tff(642,plain,
% 1.15/1.36 ((~hskp37) | c2_1(a2196)),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[641, 636])).
% 1.15/1.37 tff(643,plain,
% 1.15/1.37 (c2_1(a2196)),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[642, 629])).
% 1.15/1.37 tff(644,plain,
% 1.15/1.37 (((~hskp37) | c1_1(a2196)) <=> ((~hskp37) | c1_1(a2196))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(645,axiom,((~hskp37) | c1_1(a2196)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.15/1.37 tff(646,plain,
% 1.15/1.37 ((~hskp37) | c1_1(a2196)),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.15/1.37 tff(647,plain,
% 1.15/1.37 ((~hskp37) | c1_1(a2196)),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[646, 644])).
% 1.15/1.37 tff(648,plain,
% 1.15/1.37 ((~hskp37) | c1_1(a2196)),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[647, 644])).
% 1.15/1.37 tff(649,plain,
% 1.15/1.37 ((~hskp37) | c1_1(a2196)),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[648, 644])).
% 1.15/1.37 tff(650,plain,
% 1.15/1.37 ((~hskp37) | c1_1(a2196)),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[649, 644])).
% 1.15/1.37 tff(651,plain,
% 1.15/1.37 (c1_1(a2196)),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[650, 629])).
% 1.15/1.37 tff(652,assumption,(c3_1(a2235)), introduced(assumption)).
% 1.15/1.37 tff(653,assumption,(c2_1(a2235)), introduced(assumption)).
% 1.15/1.37 tff(654,plain,
% 1.15/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(655,plain,
% 1.15/1.37 ((hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235))) <=> (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(656,plain,
% 1.15/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[655])).
% 1.15/1.37 tff(657,plain,
% 1.15/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235)))),
% 1.15/1.37 inference(transitivity,[status(thm)],[656, 654])).
% 1.15/1.37 tff(658,plain,
% 1.15/1.37 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(659,plain,
% 1.15/1.37 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c2_1(a2196)) | (~c1_1(a2196)) | (~c2_1(a2235)) | (~c1_1(a2235)) | (~c3_1(a2235))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[658, 657])).
% 1.15/1.37 tff(660,plain,
% 1.15/1.37 (~c1_1(a2235)),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[659, 150, 72, 653, 652, 651, 643, 635, 71])).
% 1.15/1.37 tff(661,assumption,(c0_1(a2235)), introduced(assumption)).
% 1.15/1.37 tff(662,plain,
% 1.15/1.37 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(663,plain,
% 1.20/1.37 ((hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235))) <=> (hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(664,plain,
% 1.20/1.37 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235)))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[663])).
% 1.20/1.37 tff(665,plain,
% 1.20/1.37 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235))),
% 1.20/1.37 inference(transitivity,[status(thm)],[664, 662])).
% 1.20/1.37 tff(666,plain,
% 1.20/1.37 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2235) | (~c0_1(a2235)) | (~c2_1(a2235)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(667,plain,
% 1.20/1.37 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | c1_1(a2235)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.20/1.37 tff(668,plain,
% 1.20/1.37 (hskp34 | hskp33 | c1_1(a2235)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[667, 150, 661, 653, 462])).
% 1.20/1.37 tff(669,plain,
% 1.20/1.37 (hskp34),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[668, 660, 72])).
% 1.20/1.37 tff(670,plain,
% 1.20/1.37 (((~hskp34) | c3_1(a2189)) <=> ((~hskp34) | c3_1(a2189))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(671,axiom,((~hskp34) | c3_1(a2189)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.20/1.37 tff(672,plain,
% 1.20/1.37 ((~hskp34) | c3_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[671, 670])).
% 1.20/1.37 tff(673,plain,
% 1.20/1.37 ((~hskp34) | c3_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[672, 670])).
% 1.20/1.37 tff(674,plain,
% 1.20/1.37 ((~hskp34) | c3_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[673, 670])).
% 1.20/1.37 tff(675,plain,
% 1.20/1.37 ((~hskp34) | c3_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[674, 670])).
% 1.20/1.37 tff(676,plain,
% 1.20/1.37 ((~hskp34) | c3_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[675, 670])).
% 1.20/1.37 tff(677,plain,
% 1.20/1.37 (c3_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[676, 669])).
% 1.20/1.37 tff(678,plain,
% 1.20/1.37 (((~hskp34) | c1_1(a2189)) <=> ((~hskp34) | c1_1(a2189))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(679,axiom,((~hskp34) | c1_1(a2189)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.20/1.37 tff(680,plain,
% 1.20/1.37 ((~hskp34) | c1_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.20/1.37 tff(681,plain,
% 1.20/1.37 ((~hskp34) | c1_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[680, 678])).
% 1.20/1.37 tff(682,plain,
% 1.20/1.37 ((~hskp34) | c1_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[681, 678])).
% 1.20/1.37 tff(683,plain,
% 1.20/1.37 ((~hskp34) | c1_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[682, 678])).
% 1.20/1.37 tff(684,plain,
% 1.20/1.37 ((~hskp34) | c1_1(a2189)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[683, 678])).
% 1.20/1.37 tff(685,plain,
% 1.20/1.37 (c1_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[684, 669])).
% 1.20/1.37 tff(686,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(687,plain,
% 1.20/1.37 ((hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189))) <=> (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(688,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[687])).
% 1.20/1.37 tff(689,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[688, 686])).
% 1.20/1.37 tff(690,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(691,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2196) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2196)) | (~c1_1(a2196))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[690, 689])).
% 1.20/1.37 tff(692,plain,
% 1.20/1.37 (~c2_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[691, 150, 72, 651, 643, 685, 677, 635, 71])).
% 1.20/1.37 tff(693,plain,
% 1.20/1.37 (((~hskp34) | (~c0_1(a2189))) <=> ((~hskp34) | (~c0_1(a2189)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(694,plain,
% 1.20/1.37 (((~c0_1(a2189)) | (~hskp34)) <=> ((~hskp34) | (~c0_1(a2189)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(695,axiom,((~c0_1(a2189)) | (~hskp34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.20/1.37 tff(696,plain,
% 1.20/1.37 ((~hskp34) | (~c0_1(a2189))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.20/1.37 tff(697,plain,
% 1.20/1.37 ((~hskp34) | (~c0_1(a2189))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[696, 693])).
% 1.20/1.37 tff(698,plain,
% 1.20/1.37 (~c0_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[697, 669])).
% 1.20/1.37 tff(699,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(700,plain,
% 1.20/1.37 (((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189))) <=> (c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(701,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[700])).
% 1.20/1.37 tff(702,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[701, 699])).
% 1.20/1.37 tff(703,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(704,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[703, 702])).
% 1.20/1.37 tff(705,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[704, 150, 661, 653, 652, 685, 677, 698, 302, 692])).
% 1.20/1.37 tff(706,plain,((~hskp37) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(707,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[706, 628, 620, 72, 612, 493])).
% 1.20/1.37 tff(708,plain,(hskp34 | hskp33 | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(709,plain,
% 1.20/1.37 (hskp34),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[708, 99, 72, 98, 97])).
% 1.20/1.37 tff(710,plain,
% 1.20/1.37 (~c0_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[697, 709])).
% 1.20/1.37 tff(711,plain,
% 1.20/1.37 (c3_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[676, 709])).
% 1.20/1.37 tff(712,plain,
% 1.20/1.37 (c1_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[684, 709])).
% 1.20/1.37 tff(713,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(714,plain,
% 1.20/1.37 ((hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189))) <=> (hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(715,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[714])).
% 1.20/1.37 tff(716,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[715, 713])).
% 1.20/1.37 tff(717,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(718,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.20/1.37 tff(719,plain,
% 1.20/1.37 (~c2_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[718, 150, 72, 712, 711, 710, 71])).
% 1.20/1.37 tff(720,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(721,plain,
% 1.20/1.37 (((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> (c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(722,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[721])).
% 1.20/1.37 tff(723,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[722, 720])).
% 1.20/1.37 tff(724,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2186) | (~c0_1(a2186)) | (~c1_1(a2186)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(725,plain,
% 1.20/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2186) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2186)) | (~c0_1(a2186))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[724, 723])).
% 1.20/1.37 tff(726,plain,
% 1.20/1.37 (~c1_1(a2186)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[725, 150, 712, 711, 327, 710, 325, 339, 719])).
% 1.20/1.37 tff(727,plain,
% 1.20/1.37 (hskp53),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[491, 726, 327, 326, 325])).
% 1.20/1.37 tff(728,plain,
% 1.20/1.37 (c0_1(a2235)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[95, 727])).
% 1.20/1.37 tff(729,plain,
% 1.20/1.37 (c2_1(a2235)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[619, 727])).
% 1.20/1.37 tff(730,plain,
% 1.20/1.37 (c3_1(a2235)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[627, 727])).
% 1.20/1.37 tff(731,assumption,(hskp34), introduced(assumption)).
% 1.20/1.37 tff(732,plain,
% 1.20/1.37 (~c0_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[697, 731])).
% 1.20/1.37 tff(733,plain,
% 1.20/1.37 (c3_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[676, 731])).
% 1.20/1.37 tff(734,plain,
% 1.20/1.37 (c1_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[684, 731])).
% 1.20/1.37 tff(735,plain,
% 1.20/1.37 (~c2_1(a2189)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[718, 150, 72, 734, 733, 732, 71])).
% 1.20/1.37 tff(736,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[704, 150, 661, 653, 652, 734, 733, 732, 302, 735])).
% 1.20/1.37 tff(737,plain,((~hskp34) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(738,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[737, 730, 729, 72, 709, 728])).
% 1.20/1.37 tff(739,plain,(c0_1(a2181) | hskp33 | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(740,plain,
% 1.20/1.37 (c0_1(a2181)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[739, 98, 72, 97])).
% 1.20/1.37 tff(741,plain,
% 1.20/1.37 (((~hskp0) | (~c0_1(a2181))) <=> ((~hskp0) | (~c0_1(a2181)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(742,plain,
% 1.20/1.37 (((~c0_1(a2181)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2181)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(743,axiom,((~c0_1(a2181)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause239')).
% 1.20/1.37 tff(744,plain,
% 1.20/1.37 ((~hskp0) | (~c0_1(a2181))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[743, 742])).
% 1.20/1.37 tff(745,plain,
% 1.20/1.37 ((~hskp0) | (~c0_1(a2181))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[744, 741])).
% 1.20/1.37 tff(746,plain,
% 1.20/1.37 (~hskp0),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[745, 740])).
% 1.20/1.37 tff(747,plain,
% 1.20/1.37 (c2_1(a2235)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[619, 88])).
% 1.20/1.37 tff(748,plain,
% 1.20/1.37 (c1_1(a2235)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[667, 150, 328, 72, 96, 747, 462])).
% 1.20/1.37 tff(749,plain,
% 1.20/1.37 (^[U: $i] : refl((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 1.20/1.37 inference(bind,[status(th)],[])).
% 1.20/1.37 tff(750,plain,
% 1.20/1.37 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.20/1.37 inference(quant_intro,[status(thm)],[749])).
% 1.20/1.37 tff(751,plain,
% 1.20/1.37 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(752,plain,
% 1.20/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~c0_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> (((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))))), rewrite((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 1.20/1.37 inference(bind,[status(th)],[])).
% 1.20/1.37 tff(753,plain,
% 1.20/1.37 (![U: $i] : (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.20/1.37 inference(quant_intro,[status(thm)],[752])).
% 1.20/1.37 tff(754,axiom,(![U: $i] : (((((~c1_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause256')).
% 1.20/1.37 tff(755,plain,
% 1.20/1.37 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[754, 753])).
% 1.20/1.37 tff(756,plain,
% 1.20/1.37 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[755, 751])).
% 1.20/1.37 tff(757,plain,(
% 1.20/1.37 ![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.20/1.37 inference(skolemize,[status(sab)],[756])).
% 1.20/1.37 tff(758,plain,
% 1.20/1.37 (![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[757, 750])).
% 1.20/1.37 tff(759,assumption,(~hskp0), introduced(assumption)).
% 1.20/1.37 tff(760,plain,
% 1.20/1.37 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(761,plain,
% 1.20/1.37 ((hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(762,plain,
% 1.20/1.37 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[761])).
% 1.20/1.37 tff(763,plain,
% 1.20/1.37 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[762, 760])).
% 1.20/1.37 tff(764,plain,
% 1.20/1.37 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(765,plain,
% 1.20/1.37 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c1_1(a2235))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[764, 763])).
% 1.20/1.37 tff(766,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[765, 150, 759, 96, 747, 758, 748])).
% 1.20/1.37 tff(767,plain,((~hskp53) | hskp0 | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(768,plain,
% 1.20/1.37 (~hskp53),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[767, 328, 746, 72])).
% 1.20/1.37 tff(769,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(770,plain,
% 1.20/1.37 ((hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181)) <=> (hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(771,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[770])).
% 1.20/1.37 tff(772,plain,
% 1.20/1.37 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.37 inference(transitivity,[status(thm)],[771, 769])).
% 1.20/1.37 tff(773,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(774,plain,
% 1.20/1.37 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.20/1.37 tff(775,plain,
% 1.20/1.37 (hskp53 | (~c0_1(a2181)) | c3_1(a2181)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[774, 150, 98, 97, 479])).
% 1.20/1.37 tff(776,plain,
% 1.20/1.37 (c3_1(a2181)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[775, 768, 740])).
% 1.20/1.37 tff(777,plain,
% 1.20/1.37 (hskp32),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[186, 776, 98, 97])).
% 1.20/1.37 tff(778,plain,
% 1.20/1.37 (~c2_1(a2186)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[324, 777])).
% 1.20/1.37 tff(779,plain,
% 1.20/1.37 (c0_1(a2186)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[80, 777])).
% 1.20/1.37 tff(780,plain,
% 1.20/1.37 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(781,plain,
% 1.20/1.37 ((hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181))) <=> (hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(782,plain,
% 1.20/1.37 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[781])).
% 1.20/1.37 tff(783,plain,
% 1.20/1.37 (((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)))) <=> ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.37 inference(transitivity,[status(thm)],[782, 780])).
% 1.20/1.37 tff(784,plain,
% 1.20/1.37 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp46 | hskp34 | (~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(785,plain,
% 1.20/1.37 ((~![U: $i] : (hskp46 | hskp34 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp46 | hskp34 | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[784, 783])).
% 1.20/1.37 tff(786,plain,
% 1.20/1.37 (hskp46 | hskp34 | (~c0_1(a2181)) | (~c3_1(a2181))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[785, 150, 98, 416])).
% 1.20/1.37 tff(787,plain,
% 1.20/1.37 (hskp46),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[786, 776, 740, 328])).
% 1.20/1.37 tff(788,plain,
% 1.20/1.37 (c2_1(a2218)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[436, 787])).
% 1.20/1.37 tff(789,plain,
% 1.20/1.37 (c0_1(a2218)),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[444, 787])).
% 1.20/1.37 tff(790,plain,
% 1.20/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(791,plain,
% 1.20/1.38 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(792,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[791])).
% 1.20/1.38 tff(793,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[792, 790])).
% 1.20/1.38 tff(794,plain,
% 1.20/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(795,plain,
% 1.20/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[794, 793])).
% 1.20/1.38 tff(796,plain,
% 1.20/1.38 (~c1_1(a2218)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[795, 150, 789, 788, 779, 481, 778, 98, 97, 51, 776])).
% 1.20/1.38 tff(797,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[465, 150, 328, 72, 789, 788, 462, 796])).
% 1.20/1.38 tff(798,plain,(hskp34 | hskp33 | c3_1(a2186) | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(799,plain,
% 1.20/1.38 (hskp34),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[798, 481, 72, 98, 97])).
% 1.20/1.38 tff(800,plain,
% 1.20/1.38 (~c0_1(a2189)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[697, 799])).
% 1.20/1.38 tff(801,plain,
% 1.20/1.38 (c3_1(a2189)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[676, 799])).
% 1.20/1.38 tff(802,plain,
% 1.20/1.38 (c1_1(a2189)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[684, 799])).
% 1.20/1.38 tff(803,plain,
% 1.20/1.38 (~c2_1(a2189)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[718, 150, 72, 802, 801, 800, 71])).
% 1.20/1.38 tff(804,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(805,plain,
% 1.20/1.38 ((hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181))) <=> (hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(806,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[805])).
% 1.20/1.38 tff(807,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[806, 804])).
% 1.20/1.38 tff(808,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2189) | c0_1(a2189) | (~c1_1(a2189)) | c1_1(a2181) | c3_1(a2181) | (~c0_1(a2181)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(809,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c0_1(a2189) | (~c0_1(a2181)) | c1_1(a2181) | (~ndr1_0) | c3_1(a2181) | c2_1(a2189) | (~c1_1(a2189))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.20/1.38 tff(810,plain,
% 1.20/1.38 (c3_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[809, 150, 72, 802, 800, 740, 98, 246, 803])).
% 1.20/1.38 tff(811,plain,
% 1.20/1.38 (hskp32),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[186, 810, 98, 97])).
% 1.20/1.38 tff(812,plain,
% 1.20/1.38 (~c2_1(a2186)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[324, 811])).
% 1.20/1.38 tff(813,plain,
% 1.20/1.38 (c0_1(a2186)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[80, 811])).
% 1.20/1.38 tff(814,plain,
% 1.20/1.38 (~c1_1(a2186)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[725, 150, 802, 801, 813, 800, 812, 339, 803])).
% 1.20/1.38 tff(815,plain,
% 1.20/1.38 (hskp53),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[491, 814, 813, 481, 812])).
% 1.20/1.38 tff(816,plain,
% 1.20/1.38 (c0_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[95, 815])).
% 1.20/1.38 tff(817,plain,
% 1.20/1.38 (c2_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[619, 815])).
% 1.20/1.38 tff(818,plain,
% 1.20/1.38 (c3_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[627, 815])).
% 1.20/1.38 tff(819,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[737, 818, 817, 72, 799, 816])).
% 1.20/1.38 tff(820,plain,(c3_1(a2186) | hskp33 | c1_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(821,plain,
% 1.20/1.38 (c3_1(a2186)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[820, 98, 72, 97])).
% 1.20/1.38 tff(822,plain,
% 1.20/1.38 (~hskp32),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[86, 821])).
% 1.20/1.38 tff(823,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(824,plain,
% 1.20/1.38 ((hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181))) <=> (hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(825,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[824])).
% 1.20/1.38 tff(826,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[825, 823])).
% 1.20/1.38 tff(827,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2181) | c1_1(a2181) | (~c3_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~c0_1(a2181)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(828,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | (~c0_1(a2181)) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[827, 826])).
% 1.20/1.38 tff(829,plain,
% 1.20/1.38 (hskp32 | (~c0_1(a2181)) | (~c3_1(a2181))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[828, 150, 98, 97, 111])).
% 1.20/1.38 tff(830,plain,
% 1.20/1.38 (~c3_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[829, 822, 740])).
% 1.20/1.38 tff(831,plain,
% 1.20/1.38 (hskp53),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[775, 830, 740])).
% 1.20/1.38 tff(832,plain,
% 1.20/1.38 (c0_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[95, 831])).
% 1.20/1.38 tff(833,plain,
% 1.20/1.38 (hskp34),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[767, 831, 746, 72])).
% 1.20/1.38 tff(834,plain,
% 1.20/1.38 (c2_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[619, 831])).
% 1.20/1.38 tff(835,plain,
% 1.20/1.38 (c3_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[627, 831])).
% 1.20/1.38 tff(836,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[737, 835, 834, 72, 833, 832])).
% 1.20/1.38 tff(837,plain,(c1_1(a2181) | hskp33 | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(838,plain,
% 1.20/1.38 (c1_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[837, 97, 72])).
% 1.20/1.38 tff(839,assumption,(hskp55), introduced(assumption)).
% 1.20/1.38 tff(840,plain,
% 1.20/1.38 (((~hskp55) | c2_1(a2241)) <=> ((~hskp55) | c2_1(a2241))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(841,axiom,((~hskp55) | c2_1(a2241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.20/1.38 tff(842,plain,
% 1.20/1.38 ((~hskp55) | c2_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[841, 840])).
% 1.20/1.38 tff(843,plain,
% 1.20/1.38 ((~hskp55) | c2_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[842, 840])).
% 1.20/1.38 tff(844,plain,
% 1.20/1.38 ((~hskp55) | c2_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[843, 840])).
% 1.20/1.38 tff(845,plain,
% 1.20/1.38 ((~hskp55) | c2_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[844, 840])).
% 1.20/1.38 tff(846,plain,
% 1.20/1.38 ((~hskp55) | c2_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[845, 840])).
% 1.20/1.38 tff(847,plain,
% 1.20/1.38 (c2_1(a2241)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[846, 839])).
% 1.20/1.38 tff(848,plain,
% 1.20/1.38 (((~hskp55) | c0_1(a2241)) <=> ((~hskp55) | c0_1(a2241))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(849,axiom,((~hskp55) | c0_1(a2241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.20/1.38 tff(850,plain,
% 1.20/1.38 ((~hskp55) | c0_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[849, 848])).
% 1.20/1.38 tff(851,plain,
% 1.20/1.38 ((~hskp55) | c0_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[850, 848])).
% 1.20/1.38 tff(852,plain,
% 1.20/1.38 ((~hskp55) | c0_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[851, 848])).
% 1.20/1.38 tff(853,plain,
% 1.20/1.38 ((~hskp55) | c0_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[852, 848])).
% 1.20/1.38 tff(854,plain,
% 1.20/1.38 ((~hskp55) | c0_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[853, 848])).
% 1.20/1.38 tff(855,plain,
% 1.20/1.38 (c0_1(a2241)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[854, 839])).
% 1.20/1.38 tff(856,plain,
% 1.20/1.38 (((~hskp55) | c1_1(a2241)) <=> ((~hskp55) | c1_1(a2241))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(857,axiom,((~hskp55) | c1_1(a2241)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.20/1.38 tff(858,plain,
% 1.20/1.38 ((~hskp55) | c1_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.20/1.38 tff(859,plain,
% 1.20/1.38 ((~hskp55) | c1_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[858, 856])).
% 1.20/1.38 tff(860,plain,
% 1.20/1.38 ((~hskp55) | c1_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[859, 856])).
% 1.20/1.38 tff(861,plain,
% 1.20/1.38 ((~hskp55) | c1_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[860, 856])).
% 1.20/1.38 tff(862,plain,
% 1.20/1.38 ((~hskp55) | c1_1(a2241)),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[861, 856])).
% 1.20/1.38 tff(863,plain,
% 1.20/1.38 (c1_1(a2241)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[862, 839])).
% 1.20/1.38 tff(864,plain,
% 1.20/1.38 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(865,plain,
% 1.20/1.38 ((hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(866,plain,
% 1.20/1.38 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[865])).
% 1.20/1.38 tff(867,plain,
% 1.20/1.38 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[866, 864])).
% 1.20/1.38 tff(868,plain,
% 1.20/1.38 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(869,plain,
% 1.20/1.38 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.20/1.38 tff(870,plain,
% 1.20/1.38 (hskp0),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[869, 150, 863, 855, 847, 758])).
% 1.20/1.38 tff(871,plain,
% 1.20/1.38 (((~hskp0) | (~c2_1(a2181))) <=> ((~hskp0) | (~c2_1(a2181)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(872,plain,
% 1.20/1.38 (((~c2_1(a2181)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a2181)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(873,axiom,((~c2_1(a2181)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause241')).
% 1.20/1.38 tff(874,plain,
% 1.20/1.38 ((~hskp0) | (~c2_1(a2181))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.20/1.38 tff(875,plain,
% 1.20/1.38 ((~hskp0) | (~c2_1(a2181))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[874, 871])).
% 1.20/1.38 tff(876,plain,
% 1.20/1.38 (~c2_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[875, 870])).
% 1.20/1.38 tff(877,plain,
% 1.20/1.38 (((~hskp0) | (~c1_1(a2181))) <=> ((~hskp0) | (~c1_1(a2181)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(878,plain,
% 1.20/1.38 (((~c1_1(a2181)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a2181)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(879,axiom,((~c1_1(a2181)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause240')).
% 1.20/1.38 tff(880,plain,
% 1.20/1.38 ((~hskp0) | (~c1_1(a2181))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[879, 878])).
% 1.20/1.38 tff(881,plain,
% 1.20/1.38 ((~hskp0) | (~c1_1(a2181))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[880, 877])).
% 1.20/1.38 tff(882,plain,
% 1.20/1.38 (~c1_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[881, 870])).
% 1.20/1.38 tff(883,plain,
% 1.20/1.38 (~c0_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[745, 870])).
% 1.20/1.38 tff(884,assumption,(c1_1(a2241)), introduced(assumption)).
% 1.20/1.38 tff(885,assumption,(c2_1(a2241)), introduced(assumption)).
% 1.20/1.38 tff(886,assumption,(c0_1(a2241)), introduced(assumption)).
% 1.20/1.38 tff(887,plain,
% 1.20/1.38 (hskp0),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[869, 150, 884, 886, 885, 758])).
% 1.20/1.38 tff(888,plain,
% 1.20/1.38 (~c2_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[875, 887])).
% 1.20/1.38 tff(889,plain,
% 1.20/1.38 (~c1_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[881, 887])).
% 1.20/1.38 tff(890,plain,
% 1.20/1.38 (~c0_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[745, 887])).
% 1.20/1.38 tff(891,plain,
% 1.20/1.38 (~c2_1(a2186)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[324, 73])).
% 1.20/1.38 tff(892,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(893,plain,
% 1.20/1.38 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181)) <=> (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(894,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[893])).
% 1.20/1.38 tff(895,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[894, 892])).
% 1.20/1.38 tff(896,plain,
% 1.20/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(897,plain,
% 1.20/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2186) | c2_1(a2186) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2186))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[896, 895])).
% 1.20/1.38 tff(898,plain,
% 1.20/1.38 (~c1_1(a2186)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[897, 150, 884, 886, 885, 87, 891, 890, 889, 888, 542])).
% 1.20/1.38 tff(899,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[489, 150, 483, 81, 87, 891, 479, 898])).
% 1.20/1.38 tff(900,plain,((~hskp32) | hskp53 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(901,plain,
% 1.20/1.38 (~hskp32),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[900, 483, 884, 886, 885])).
% 1.20/1.38 tff(902,plain,
% 1.20/1.38 (hskp58 | (~c3_1(a2181))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[156, 150, 889, 888, 121])).
% 1.20/1.38 tff(903,plain,
% 1.20/1.38 (hskp58),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[902, 101])).
% 1.20/1.38 tff(904,plain,
% 1.20/1.38 (~c2_1(a2252)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[169, 903])).
% 1.20/1.38 tff(905,plain,
% 1.20/1.38 (c0_1(a2252)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[177, 903])).
% 1.20/1.38 tff(906,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(907,plain,
% 1.20/1.38 (((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241))) <=> (c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(908,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[907])).
% 1.20/1.38 tff(909,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[908, 906])).
% 1.20/1.38 tff(910,plain,
% 1.20/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c3_1(a2252) | (~c0_1(a2252)) | c1_1(a2181) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(911,plain,
% 1.20/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c3_1(a2252) | (~c0_1(a2252))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[910, 909])).
% 1.20/1.38 tff(912,plain,
% 1.20/1.38 (c3_1(a2252)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[911, 150, 905, 884, 886, 885, 904, 889, 888, 51, 101])).
% 1.20/1.38 tff(913,plain,
% 1.20/1.38 (~c1_1(a2252)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[163, 903])).
% 1.20/1.38 tff(914,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(915,plain,
% 1.20/1.38 ((hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(916,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[915])).
% 1.20/1.38 tff(917,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[916, 914])).
% 1.20/1.38 tff(918,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(919,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | (~c3_1(a2252)) | (~c0_1(a2252))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[918, 917])).
% 1.20/1.38 tff(920,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[919, 150, 100, 905, 904, 913, 111, 912])).
% 1.20/1.38 tff(921,plain,((~c3_1(a2181)) | hskp32 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(922,plain,
% 1.20/1.38 (~c3_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[921, 901, 884, 886, 885])).
% 1.20/1.38 tff(923,plain,
% 1.20/1.38 (hskp32 | hskp2 | c3_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[213, 150, 890, 889, 207])).
% 1.20/1.38 tff(924,plain,
% 1.20/1.38 (hskp2),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[923, 922, 901])).
% 1.20/1.38 tff(925,plain,
% 1.20/1.38 (~c2_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[220, 924])).
% 1.20/1.38 tff(926,plain,
% 1.20/1.38 (c3_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[228, 924])).
% 1.20/1.38 tff(927,plain,
% 1.20/1.38 (~c0_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[235, 150, 926, 925, 890, 889, 888, 197, 922])).
% 1.20/1.38 tff(928,plain,
% 1.20/1.38 (hskp47),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[262, 150, 926, 925, 889, 888, 256, 922, 927])).
% 1.20/1.38 tff(929,plain,
% 1.20/1.38 (~c1_1(a2226)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[268, 928])).
% 1.20/1.38 tff(930,plain,
% 1.20/1.38 (c0_1(a2226)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[284, 928])).
% 1.20/1.38 tff(931,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(932,plain,
% 1.20/1.38 ((hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181)) <=> (hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(933,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[932])).
% 1.20/1.38 tff(934,plain,
% 1.20/1.38 (((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226)))),
% 1.20/1.38 inference(transitivity,[status(thm)],[933, 931])).
% 1.20/1.38 tff(935,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp53 | (~ndr1_0) | c1_1(a2226) | c3_1(a2226) | (~c0_1(a2226)) | c1_1(a2181) | c3_1(a2181) | c2_1(a2181))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(936,plain,
% 1.20/1.38 ((~![V: $i, U: $i] : (hskp53 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp53 | c1_1(a2226) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181) | c3_1(a2226) | (~c0_1(a2226))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[935, 934])).
% 1.20/1.38 tff(937,plain,
% 1.20/1.38 (c3_1(a2226)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[936, 150, 483, 930, 929, 889, 888, 479, 922])).
% 1.20/1.38 tff(938,plain,
% 1.20/1.38 (c1_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[276, 924])).
% 1.20/1.38 tff(939,plain,
% 1.20/1.38 (c2_1(a2226)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[309, 928])).
% 1.20/1.38 tff(940,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[316, 150, 939, 930, 926, 938, 925, 302, 927, 937])).
% 1.20/1.38 tff(941,plain,(hskp53 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(942,plain,
% 1.20/1.38 (hskp53),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[941, 884, 886, 885])).
% 1.20/1.38 tff(943,plain,
% 1.20/1.38 (c0_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[95, 942])).
% 1.20/1.38 tff(944,plain,
% 1.20/1.38 (c3_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[627, 942])).
% 1.20/1.38 tff(945,plain,
% 1.20/1.38 (c2_1(a2235)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[619, 942])).
% 1.20/1.38 tff(946,plain,
% 1.20/1.38 (~hskp34),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[737, 72, 945, 944, 943])).
% 1.20/1.38 tff(947,plain,
% 1.20/1.38 (~c3_1(a2181)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[921, 100, 884, 886, 885])).
% 1.20/1.38 tff(948,plain,
% 1.20/1.38 (hskp2),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[923, 947, 100])).
% 1.20/1.38 tff(949,plain,
% 1.20/1.38 (~c2_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[220, 948])).
% 1.20/1.38 tff(950,plain,
% 1.20/1.38 (c3_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[228, 948])).
% 1.20/1.38 tff(951,plain,
% 1.20/1.38 (~c0_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[235, 150, 950, 949, 890, 889, 888, 197, 947])).
% 1.20/1.38 tff(952,plain,
% 1.20/1.38 (c1_1(a2187)),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[276, 948])).
% 1.20/1.38 tff(953,plain,
% 1.20/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(954,plain,
% 1.20/1.39 (((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187))) <=> (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(955,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[954])).
% 1.20/1.39 tff(956,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[955, 953])).
% 1.20/1.39 tff(957,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2235)) | (~c0_1(a2235)) | (~c2_1(a2235)) | c0_1(a2187) | c2_1(a2187) | (~c1_1(a2187)) | c0_1(a2187) | c2_1(a2187) | (~c3_1(a2187)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(958,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c0_1(a2235)) | (~c2_1(a2235)) | (~c3_1(a2235))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.20/1.39 tff(959,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[958, 150, 943, 945, 944, 950, 952, 949, 302, 951])).
% 1.20/1.39 tff(960,plain,(hskp32 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(961,plain,
% 1.20/1.39 (hskp32),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[960, 884, 886, 885])).
% 1.20/1.39 tff(962,plain,
% 1.20/1.39 (~c2_1(a2186)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[324, 961])).
% 1.20/1.39 tff(963,plain,
% 1.20/1.39 (~c3_1(a2186)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[86, 961])).
% 1.20/1.39 tff(964,plain,
% 1.20/1.39 (~c1_1(a2186)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[897, 150, 884, 886, 885, 963, 962, 890, 889, 888, 542])).
% 1.20/1.39 tff(965,plain,
% 1.20/1.39 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 1.20/1.39 inference(bind,[status(th)],[])).
% 1.20/1.39 tff(966,plain,
% 1.20/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.20/1.39 inference(quant_intro,[status(thm)],[965])).
% 1.20/1.39 tff(967,plain,
% 1.20/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(968,plain,
% 1.20/1.39 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 1.20/1.39 inference(bind,[status(th)],[])).
% 1.20/1.39 tff(969,plain,
% 1.20/1.39 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.20/1.39 inference(quant_intro,[status(thm)],[968])).
% 1.20/1.39 tff(970,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c0_1(U)) | c1_1(U)) | c3_1(V)) | c3_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause288')).
% 1.20/1.39 tff(971,plain,
% 1.20/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[970, 969])).
% 1.20/1.39 tff(972,plain,
% 1.20/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[971, 967])).
% 1.20/1.39 tff(973,plain,(
% 1.20/1.39 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.20/1.39 inference(skolemize,[status(sab)],[972])).
% 1.20/1.39 tff(974,plain,
% 1.20/1.39 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[973, 966])).
% 1.20/1.39 tff(975,plain,
% 1.20/1.39 (~hskp37),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[706, 72, 945, 944, 943])).
% 1.20/1.39 tff(976,plain,
% 1.20/1.39 (hskp6),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[567, 328, 975])).
% 1.20/1.39 tff(977,plain,
% 1.20/1.39 (~c1_1(a2197)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[573, 976])).
% 1.20/1.39 tff(978,plain,
% 1.20/1.39 (~c0_1(a2197)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[579, 976])).
% 1.20/1.39 tff(979,plain,
% 1.20/1.39 (c0_1(a2186)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[80, 961])).
% 1.20/1.39 tff(980,plain,
% 1.20/1.39 (hskp37 | hskp7),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[510, 150, 979, 963, 962, 504])).
% 1.20/1.39 tff(981,plain,
% 1.20/1.39 (hskp7),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[980, 975])).
% 1.20/1.39 tff(982,plain,
% 1.20/1.39 (~c3_1(a2198)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[585, 981])).
% 1.20/1.39 tff(983,plain,
% 1.20/1.39 (c0_1(a2198)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[519, 981])).
% 1.20/1.39 tff(984,plain,
% 1.20/1.39 (c2_1(a2198)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[527, 981])).
% 1.20/1.39 tff(985,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(986,plain,
% 1.20/1.39 (((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186))) <=> (c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(987,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[986])).
% 1.20/1.39 tff(988,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[987, 985])).
% 1.20/1.39 tff(989,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2197) | c0_1(a2197) | (~c2_1(a2197)) | c3_1(a2198) | (~c0_1(a2198)) | (~c2_1(a2198)) | c3_1(a2186) | c1_1(a2186) | (~c0_1(a2186)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(990,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2186) | c3_1(a2198) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c2_1(a2197)) | (~c0_1(a2198)) | (~c2_1(a2198)) | c1_1(a2186) | (~c0_1(a2186))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[989, 988])).
% 1.20/1.39 tff(991,plain,
% 1.20/1.39 (~c2_1(a2197)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[990, 150, 979, 984, 983, 963, 982, 978, 977, 974, 964])).
% 1.20/1.39 tff(992,plain,
% 1.20/1.39 (((~hskp6) | (~c3_1(a2197))) <=> ((~hskp6) | (~c3_1(a2197)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(993,plain,
% 1.20/1.39 (((~c3_1(a2197)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a2197)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(994,axiom,((~c3_1(a2197)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause228')).
% 1.20/1.39 tff(995,plain,
% 1.20/1.39 ((~hskp6) | (~c3_1(a2197))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[994, 993])).
% 1.20/1.39 tff(996,plain,
% 1.20/1.39 ((~hskp6) | (~c3_1(a2197))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[995, 992])).
% 1.20/1.39 tff(997,plain,
% 1.20/1.39 (~c3_1(a2197)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[996, 976])).
% 1.20/1.39 tff(998,plain,
% 1.20/1.39 (hskp34 | c1_1(a2198)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[531, 150, 72, 984, 983, 462])).
% 1.20/1.39 tff(999,plain,
% 1.20/1.39 (c1_1(a2198)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[998, 328])).
% 1.20/1.39 tff(1000,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1001,plain,
% 1.20/1.39 ((hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181)) <=> (hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1002,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1001])).
% 1.20/1.39 tff(1003,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1002, 1000])).
% 1.20/1.39 tff(1004,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c3_1(a2198) | (~c1_1(a2198)) | (~c0_1(a2198)) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1005,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c2_1(V))) | hskp38 | c3_1(a2198) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2198)) | (~c0_1(a2198))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 1.20/1.39 tff(1006,plain,
% 1.20/1.39 (hskp38 | (~c1_1(a2198))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1005, 150, 983, 982, 890, 889, 888, 363])).
% 1.20/1.39 tff(1007,plain,
% 1.20/1.39 (hskp38),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1006, 999])).
% 1.20/1.39 tff(1008,plain,
% 1.20/1.39 (~c2_1(a2200)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[376, 1007])).
% 1.20/1.39 tff(1009,plain,
% 1.20/1.39 (~c0_1(a2200)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[382, 1007])).
% 1.20/1.39 tff(1010,assumption,(~hskp47), introduced(assumption)).
% 1.20/1.39 tff(1011,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1012,plain,
% 1.20/1.39 ((hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197)) <=> (hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1013,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1012])).
% 1.20/1.39 tff(1014,plain,
% 1.20/1.39 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1013, 1011])).
% 1.20/1.39 tff(1015,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2200) | c0_1(a2200) | (~c3_1(a2200)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1016,plain,
% 1.20/1.39 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c0_1(a2200) | c2_1(a2200) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0) | c2_1(a2197) | (~c3_1(a2200))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 1.20/1.39 tff(1017,plain,
% 1.20/1.39 (~c3_1(a2200)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1016, 150, 1010, 1009, 1008, 997, 977, 256, 991])).
% 1.20/1.39 tff(1018,plain,
% 1.20/1.39 (c1_1(a2200)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[398, 1007])).
% 1.20/1.39 tff(1019,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1020,plain,
% 1.20/1.39 (((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197)) <=> (c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1021,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200)))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1020])).
% 1.20/1.39 tff(1022,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1021, 1019])).
% 1.20/1.39 tff(1023,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2197) | c2_1(a2197) | c1_1(a2197))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1024,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c2_1(a2200) | c0_1(a2197) | c1_1(a2197) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | c2_1(a2197) | (~c1_1(a2200)) | c3_1(a2200)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 1.20/1.39 tff(1025,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1024, 150, 884, 886, 885, 1018, 1008, 978, 977, 542, 1017, 991])).
% 1.20/1.39 tff(1026,plain,(hskp34 | (~c1_1(a2241)) | (~c0_1(a2241)) | (~c2_1(a2241)) | hskp47 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(1027,plain,
% 1.20/1.39 (hskp47),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1026, 946, 886, 885, 884, 72])).
% 1.20/1.39 tff(1028,plain,
% 1.20/1.39 (~c1_1(a2226)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[268, 1027])).
% 1.20/1.39 tff(1029,plain,
% 1.20/1.39 (c0_1(a2226)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[284, 1027])).
% 1.20/1.39 tff(1030,plain,
% 1.20/1.39 (c2_1(a2226)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[309, 1027])).
% 1.20/1.39 tff(1031,plain,
% 1.20/1.39 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1032,plain,
% 1.20/1.39 ((hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226))) <=> (hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1033,plain,
% 1.20/1.39 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1032])).
% 1.20/1.39 tff(1034,plain,
% 1.20/1.39 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1033, 1031])).
% 1.20/1.39 tff(1035,plain,
% 1.20/1.39 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2226) | (~c0_1(a2226)) | (~c2_1(a2226)))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1036,plain,
% 1.20/1.39 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | c1_1(a2226) | (~ndr1_0) | (~c2_1(a2226)) | (~c0_1(a2226))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.20/1.39 tff(1037,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1036, 150, 946, 72, 1030, 1029, 1028, 462])).
% 1.20/1.39 tff(1038,plain,(hskp33 | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(1039,plain,
% 1.20/1.39 (hskp33),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1038, 855, 847, 863])).
% 1.20/1.39 tff(1040,plain,
% 1.20/1.39 (((~hskp33) | (~c2_1(a2188))) <=> ((~hskp33) | (~c2_1(a2188)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1041,plain,
% 1.20/1.39 (((~c2_1(a2188)) | (~hskp33)) <=> ((~hskp33) | (~c2_1(a2188)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1042,axiom,((~c2_1(a2188)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.20/1.39 tff(1043,plain,
% 1.20/1.39 ((~hskp33) | (~c2_1(a2188))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 1.20/1.39 tff(1044,plain,
% 1.20/1.39 ((~hskp33) | (~c2_1(a2188))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1043, 1040])).
% 1.20/1.39 tff(1045,plain,
% 1.20/1.39 (~c2_1(a2188)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1044, 1039])).
% 1.20/1.39 tff(1046,plain,
% 1.20/1.39 (((~hskp33) | (~c3_1(a2188))) <=> ((~hskp33) | (~c3_1(a2188)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1047,plain,
% 1.20/1.39 (((~c3_1(a2188)) | (~hskp33)) <=> ((~hskp33) | (~c3_1(a2188)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1048,axiom,((~c3_1(a2188)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.20/1.39 tff(1049,plain,
% 1.20/1.39 ((~hskp33) | (~c3_1(a2188))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 1.20/1.39 tff(1050,plain,
% 1.20/1.39 ((~hskp33) | (~c3_1(a2188))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1049, 1046])).
% 1.20/1.39 tff(1051,plain,
% 1.20/1.39 (~c3_1(a2188)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1050, 1039])).
% 1.20/1.39 tff(1052,plain,
% 1.20/1.39 (((~hskp33) | c1_1(a2188)) <=> ((~hskp33) | c1_1(a2188))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1053,axiom,((~hskp33) | c1_1(a2188)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.20/1.39 tff(1054,plain,
% 1.20/1.39 ((~hskp33) | c1_1(a2188)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.20/1.39 tff(1055,plain,
% 1.20/1.39 ((~hskp33) | c1_1(a2188)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1054, 1052])).
% 1.20/1.39 tff(1056,plain,
% 1.20/1.39 ((~hskp33) | c1_1(a2188)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1055, 1052])).
% 1.20/1.39 tff(1057,plain,
% 1.20/1.39 ((~hskp33) | c1_1(a2188)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1056, 1052])).
% 1.20/1.39 tff(1058,plain,
% 1.20/1.39 ((~hskp33) | c1_1(a2188)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1057, 1052])).
% 1.20/1.39 tff(1059,plain,
% 1.20/1.39 (c1_1(a2188)),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1058, 1039])).
% 1.20/1.39 tff(1060,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1061,plain,
% 1.20/1.39 (((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181)) <=> (c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1062,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | (c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1061])).
% 1.20/1.39 tff(1063,plain,
% 1.20/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188)))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1062, 1060])).
% 1.20/1.39 tff(1064,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)) | (~c0_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2241)) | c0_1(a2181) | c2_1(a2181) | c1_1(a2181))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1065,plain,
% 1.20/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c0_1(V)) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | c1_1(W))) | c3_1(a2188) | c2_1(a2188) | c0_1(a2181) | c1_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c0_1(a2241)) | (~c1_1(a2241)) | (~c2_1(a2241)) | (~c1_1(a2188))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 1.20/1.39 tff(1066,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1065, 150, 863, 855, 847, 1059, 1051, 1045, 883, 882, 876, 542])).
% 1.20/1.39 tff(1067,plain,(~hskp55), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(1068,assumption,(hskp26), introduced(assumption)).
% 1.20/1.39 tff(1069,plain,
% 1.20/1.39 (((~hskp26) | c2_1(a2178)) <=> ((~hskp26) | c2_1(a2178))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1070,axiom,((~hskp26) | c2_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.20/1.39 tff(1071,plain,
% 1.20/1.39 ((~hskp26) | c2_1(a2178)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 1.20/1.39 tff(1072,plain,
% 1.20/1.39 ((~hskp26) | c2_1(a2178)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1071, 1069])).
% 1.20/1.39 tff(1073,plain,
% 1.20/1.39 ((~hskp26) | c2_1(a2178)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1072, 1069])).
% 1.20/1.39 tff(1074,plain,
% 1.20/1.39 ((~hskp26) | c2_1(a2178)),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1073, 1069])).
% 1.20/1.40 tff(1075,plain,
% 1.20/1.40 ((~hskp26) | c2_1(a2178)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1074, 1069])).
% 1.20/1.40 tff(1076,plain,
% 1.20/1.40 (c2_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1075, 1068])).
% 1.20/1.40 tff(1077,plain,
% 1.20/1.40 (((~hskp26) | c0_1(a2178)) <=> ((~hskp26) | c0_1(a2178))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1078,axiom,((~hskp26) | c0_1(a2178)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.20/1.40 tff(1079,plain,
% 1.20/1.40 ((~hskp26) | c0_1(a2178)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.20/1.40 tff(1080,plain,
% 1.20/1.40 ((~hskp26) | c0_1(a2178)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1079, 1077])).
% 1.20/1.40 tff(1081,plain,
% 1.20/1.40 ((~hskp26) | c0_1(a2178)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1080, 1077])).
% 1.20/1.40 tff(1082,plain,
% 1.20/1.40 ((~hskp26) | c0_1(a2178)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1081, 1077])).
% 1.20/1.40 tff(1083,plain,
% 1.20/1.40 ((~hskp26) | c0_1(a2178)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1082, 1077])).
% 1.20/1.40 tff(1084,plain,
% 1.20/1.40 (c0_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1083, 1068])).
% 1.20/1.40 tff(1085,plain,
% 1.20/1.40 (~hskp0),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[881, 838])).
% 1.20/1.40 tff(1086,plain,
% 1.20/1.40 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1087,plain,
% 1.20/1.40 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1088,plain,
% 1.20/1.40 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c1_1(a2178)) | (~c0_1(a2178)) | (~c2_1(a2178))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.20/1.40 tff(1089,plain,
% 1.20/1.40 (~c1_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1088, 150, 1085, 1084, 1076, 758])).
% 1.20/1.40 tff(1090,plain,
% 1.20/1.40 (((~hskp26) | (~c3_1(a2178))) <=> ((~hskp26) | (~c3_1(a2178)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1091,plain,
% 1.20/1.40 (((~c3_1(a2178)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a2178)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1092,axiom,((~c3_1(a2178)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.20/1.40 tff(1093,plain,
% 1.20/1.40 ((~hskp26) | (~c3_1(a2178))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 1.20/1.40 tff(1094,plain,
% 1.20/1.40 ((~hskp26) | (~c3_1(a2178))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1093, 1090])).
% 1.20/1.40 tff(1095,plain,
% 1.20/1.40 (~c3_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1094, 1068])).
% 1.20/1.40 tff(1096,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1097,plain,
% 1.20/1.40 ((hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178))) <=> (hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1098,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1097])).
% 1.20/1.40 tff(1099,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1098, 1096])).
% 1.20/1.40 tff(1100,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2178) | c3_1(a2178) | (~c0_1(a2178)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1101,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c3_1(a2178) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 1.20/1.40 tff(1102,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1101, 150, 72, 1084, 1095, 99, 838, 97, 246, 1089])).
% 1.20/1.40 tff(1103,plain,((~hskp26) | hskp33 | c0_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1104,plain,
% 1.20/1.40 (~hskp26),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1103, 99, 72, 97])).
% 1.20/1.40 tff(1105,assumption,(hskp48), introduced(assumption)).
% 1.20/1.40 tff(1106,plain,
% 1.20/1.40 (((~hskp48) | (~c0_1(a2228))) <=> ((~hskp48) | (~c0_1(a2228)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1107,plain,
% 1.20/1.40 (((~c0_1(a2228)) | (~hskp48)) <=> ((~hskp48) | (~c0_1(a2228)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1108,axiom,((~c0_1(a2228)) | (~hskp48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.20/1.40 tff(1109,plain,
% 1.20/1.40 ((~hskp48) | (~c0_1(a2228))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.20/1.40 tff(1110,plain,
% 1.20/1.40 ((~hskp48) | (~c0_1(a2228))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1109, 1106])).
% 1.20/1.40 tff(1111,plain,
% 1.20/1.40 (~c0_1(a2228)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1110, 1105])).
% 1.20/1.40 tff(1112,plain,
% 1.20/1.40 (((~hskp48) | c2_1(a2228)) <=> ((~hskp48) | c2_1(a2228))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1113,axiom,((~hskp48) | c2_1(a2228)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.20/1.40 tff(1114,plain,
% 1.20/1.40 ((~hskp48) | c2_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.20/1.40 tff(1115,plain,
% 1.20/1.40 ((~hskp48) | c2_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1114, 1112])).
% 1.20/1.40 tff(1116,plain,
% 1.20/1.40 ((~hskp48) | c2_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1115, 1112])).
% 1.20/1.40 tff(1117,plain,
% 1.20/1.40 ((~hskp48) | c2_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1116, 1112])).
% 1.20/1.40 tff(1118,plain,
% 1.20/1.40 ((~hskp48) | c2_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1117, 1112])).
% 1.20/1.40 tff(1119,plain,
% 1.20/1.40 (c2_1(a2228)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1118, 1105])).
% 1.20/1.40 tff(1120,plain,
% 1.20/1.40 (((~hskp48) | c3_1(a2228)) <=> ((~hskp48) | c3_1(a2228))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1121,axiom,((~hskp48) | c3_1(a2228)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.20/1.40 tff(1122,plain,
% 1.20/1.40 ((~hskp48) | c3_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.20/1.40 tff(1123,plain,
% 1.20/1.40 ((~hskp48) | c3_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1122, 1120])).
% 1.20/1.40 tff(1124,plain,
% 1.20/1.40 ((~hskp48) | c3_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1123, 1120])).
% 1.20/1.40 tff(1125,plain,
% 1.20/1.40 ((~hskp48) | c3_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1124, 1120])).
% 1.20/1.40 tff(1126,plain,
% 1.20/1.40 ((~hskp48) | c3_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1125, 1120])).
% 1.20/1.40 tff(1127,plain,
% 1.20/1.40 (c3_1(a2228)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1126, 1105])).
% 1.20/1.40 tff(1128,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1129,plain,
% 1.20/1.40 ((hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228))) <=> (hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1130,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1129])).
% 1.20/1.40 tff(1131,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1130, 1128])).
% 1.20/1.40 tff(1132,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c2_1(a2228)) | (~c1_1(a2228)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1133,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c1_1(a2228)) | (~c3_1(a2228))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 1.20/1.40 tff(1134,plain,
% 1.20/1.40 (~c1_1(a2228)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1133, 150, 72, 1127, 1119, 1111, 71])).
% 1.20/1.40 tff(1135,plain,
% 1.20/1.40 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 1.20/1.40 inference(bind,[status(th)],[])).
% 1.20/1.40 tff(1136,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.20/1.40 inference(quant_intro,[status(thm)],[1135])).
% 1.20/1.40 tff(1137,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1138,plain,
% 1.20/1.40 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp26))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 1.20/1.40 inference(bind,[status(th)],[])).
% 1.20/1.40 tff(1139,plain,
% 1.20/1.40 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.20/1.40 inference(quant_intro,[status(thm)],[1138])).
% 1.20/1.40 tff(1140,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause272')).
% 1.20/1.40 tff(1141,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 1.20/1.40 tff(1142,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1141, 1137])).
% 1.20/1.40 tff(1143,plain,(
% 1.20/1.40 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.20/1.40 inference(skolemize,[status(sab)],[1142])).
% 1.20/1.40 tff(1144,plain,
% 1.20/1.40 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1143, 1136])).
% 1.20/1.40 tff(1145,assumption,(c1_1(a2181)), introduced(assumption)).
% 1.20/1.40 tff(1146,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1147,plain,
% 1.20/1.40 ((hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1148,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228)))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1147])).
% 1.20/1.40 tff(1149,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1148, 1146])).
% 1.20/1.40 tff(1150,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1151,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2228)) | c1_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.20/1.40 tff(1152,plain,
% 1.20/1.40 (hskp26),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1151, 150, 1119, 1111, 99, 1145, 1144, 101, 1134])).
% 1.20/1.40 tff(1153,plain,
% 1.20/1.40 (~c3_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1094, 1152])).
% 1.20/1.40 tff(1154,plain,
% 1.20/1.40 (c2_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1075, 1152])).
% 1.20/1.40 tff(1155,plain,
% 1.20/1.40 (c0_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1083, 1152])).
% 1.20/1.40 tff(1156,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1157,plain,
% 1.20/1.40 (((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178))) <=> (c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1158,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228)))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1157])).
% 1.20/1.40 tff(1159,plain,
% 1.20/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1158, 1156])).
% 1.20/1.40 tff(1160,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2228) | c0_1(a2228) | (~c2_1(a2228)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1161,plain,
% 1.20/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c0_1(a2228) | c3_1(a2178) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | (~c2_1(a2228)) | c1_1(a2228)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.20/1.40 tff(1162,plain,
% 1.20/1.40 (c1_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1161, 150, 1119, 1155, 1154, 1111, 1153, 974, 1134])).
% 1.20/1.40 tff(1163,plain,
% 1.20/1.40 (~hskp0),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[881, 1145])).
% 1.20/1.40 tff(1164,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1088, 150, 1163, 1155, 1154, 758, 1162])).
% 1.20/1.40 tff(1165,plain,((~hskp48) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1166,plain,
% 1.20/1.40 (~hskp48),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1165, 101, 838, 99, 72])).
% 1.20/1.40 tff(1167,assumption,(~hskp48), introduced(assumption)).
% 1.20/1.40 tff(1168,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1169,plain,
% 1.20/1.40 ((hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181))) <=> (hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1170,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1169])).
% 1.20/1.40 tff(1171,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1170, 1168])).
% 1.20/1.40 tff(1172,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c2_1(a2196)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1173,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2196) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2196)) | (~c1_1(a2196))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 1.20/1.40 tff(1174,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1173, 150, 1167, 651, 643, 635, 99, 1145, 41, 101])).
% 1.20/1.40 tff(1175,plain,((~hskp37) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1176,plain,
% 1.20/1.40 (~hskp37),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1175, 1166, 99, 838, 101])).
% 1.20/1.40 tff(1177,plain,
% 1.20/1.40 (hskp6),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[567, 1176, 328])).
% 1.20/1.40 tff(1178,plain,
% 1.20/1.40 (~c1_1(a2197)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[573, 1177])).
% 1.20/1.40 tff(1179,plain,
% 1.20/1.40 (~c3_1(a2197)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[996, 1177])).
% 1.20/1.40 tff(1180,assumption,(hskp47), introduced(assumption)).
% 1.20/1.40 tff(1181,plain,
% 1.20/1.40 (~c1_1(a2226)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[268, 1180])).
% 1.20/1.40 tff(1182,plain,
% 1.20/1.40 (c0_1(a2226)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[284, 1180])).
% 1.20/1.40 tff(1183,plain,
% 1.20/1.40 (c2_1(a2226)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[309, 1180])).
% 1.20/1.40 tff(1184,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1036, 150, 328, 72, 1183, 1182, 1181, 462])).
% 1.20/1.40 tff(1185,plain,((~hskp47) | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1186,plain,
% 1.20/1.40 (~hskp47),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1185, 328, 72])).
% 1.20/1.40 tff(1187,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1188,plain,
% 1.20/1.40 ((hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197)) <=> (hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1189,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197)))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1188])).
% 1.20/1.40 tff(1190,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1189, 1187])).
% 1.20/1.40 tff(1191,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c3_1(a2181)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1192,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c0_1(a2181) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2197)),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 1.20/1.40 tff(1193,plain,
% 1.20/1.40 (c2_1(a2197)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1192, 150, 1186, 1179, 1178, 99, 97, 256, 101])).
% 1.20/1.40 tff(1194,plain,
% 1.20/1.40 (~c0_1(a2197)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[579, 1177])).
% 1.20/1.40 tff(1195,plain,
% 1.20/1.40 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1196,plain,
% 1.20/1.40 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1197,plain,
% 1.20/1.40 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 1.20/1.40 tff(1198,plain,
% 1.20/1.40 (c1_1(a2178)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1197, 150, 328, 72, 1084, 1076, 462])).
% 1.20/1.40 tff(1199,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1088, 150, 759, 1084, 1076, 758, 1198])).
% 1.20/1.40 tff(1200,plain,((~hskp26) | hskp0 | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1201,plain,
% 1.20/1.40 (~hskp26),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1200, 328, 1085, 72])).
% 1.20/1.40 tff(1202,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1203,plain,
% 1.20/1.40 ((hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197))) <=> (hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1204,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1203])).
% 1.20/1.40 tff(1205,plain,
% 1.20/1.40 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1204, 1202])).
% 1.20/1.40 tff(1206,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1207,plain,
% 1.20/1.40 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2197) | c1_1(a2197) | c0_1(a2181) | (~c1_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 1.20/1.40 tff(1208,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1207, 150, 1201, 1194, 1178, 99, 838, 1144, 101, 1193])).
% 1.20/1.40 tff(1209,plain,((~c3_1(a2181)) | c0_1(a2181) | c2_1(a2181) | hskp34 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1210,plain,
% 1.20/1.40 (~c3_1(a2181)),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1209, 328, 97, 99, 72])).
% 1.20/1.40 tff(1211,plain,
% 1.20/1.40 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1212,plain,
% 1.20/1.40 ((hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181))) <=> (hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1213,plain,
% 1.20/1.41 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1212])).
% 1.20/1.41 tff(1214,plain,
% 1.20/1.41 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1213, 1211])).
% 1.20/1.41 tff(1215,plain,
% 1.20/1.41 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2181) | c3_1(a2181) | (~c1_1(a2181)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1216,plain,
% 1.20/1.41 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2181)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.20/1.41 tff(1217,plain,
% 1.20/1.41 (hskp18 | (~c1_1(a2181)) | c3_1(a2181)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1216, 150, 97, 61])).
% 1.20/1.41 tff(1218,plain,
% 1.20/1.41 (hskp18),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1217, 1210, 838])).
% 1.20/1.41 tff(1219,plain,
% 1.20/1.41 (~c2_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[352, 1218])).
% 1.20/1.41 tff(1220,plain,
% 1.20/1.41 (c3_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[390, 1218])).
% 1.20/1.41 tff(1221,plain,
% 1.20/1.41 (c0_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[423, 1218])).
% 1.20/1.41 tff(1222,plain,
% 1.20/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1223,plain,
% 1.20/1.41 (((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181))) <=> (c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1224,plain,
% 1.20/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1223])).
% 1.20/1.41 tff(1225,plain,
% 1.20/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1224, 1222])).
% 1.20/1.41 tff(1226,plain,
% 1.20/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2181) | c2_1(a2181) | (~c1_1(a2181)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1227,plain,
% 1.20/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 1.20/1.41 tff(1228,plain,
% 1.20/1.41 (~c1_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1227, 150, 1221, 1220, 1219, 99, 838, 97, 339])).
% 1.20/1.41 tff(1229,assumption,(hskp18), introduced(assumption)).
% 1.20/1.41 tff(1230,plain,
% 1.20/1.41 (~c2_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[352, 1229])).
% 1.20/1.41 tff(1231,plain,
% 1.20/1.41 (c3_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[390, 1229])).
% 1.20/1.41 tff(1232,plain,
% 1.20/1.41 (c0_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[423, 1229])).
% 1.20/1.41 tff(1233,plain,
% 1.20/1.41 (~c1_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1227, 150, 1232, 1231, 1230, 99, 1145, 97, 339])).
% 1.20/1.41 tff(1234,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1235,plain,
% 1.20/1.41 ((hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222))) <=> (hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1236,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1235])).
% 1.20/1.41 tff(1237,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.20/1.41 tff(1238,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2222) | c2_1(a2222) | (~c0_1(a2222)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1239,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.20/1.41 tff(1240,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1239, 150, 100, 1232, 1231, 1230, 111, 1233])).
% 1.20/1.41 tff(1241,plain,((~hskp18) | hskp32 | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1242,plain,
% 1.20/1.41 (hskp32),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1241, 1218, 99, 838, 97])).
% 1.20/1.41 tff(1243,plain,
% 1.20/1.41 (~c2_1(a2186)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[324, 1242])).
% 1.20/1.41 tff(1244,plain,
% 1.20/1.41 (~c3_1(a2186)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[86, 1242])).
% 1.20/1.41 tff(1245,plain,
% 1.20/1.41 (c0_1(a2186)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[80, 1242])).
% 1.20/1.41 tff(1246,plain,
% 1.20/1.41 (hskp46 | c1_1(a2222)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[427, 150, 328, 1221, 1220, 416])).
% 1.20/1.41 tff(1247,plain,
% 1.20/1.41 (hskp46),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1246, 1228])).
% 1.20/1.41 tff(1248,plain,
% 1.20/1.41 (c2_1(a2218)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[436, 1247])).
% 1.20/1.41 tff(1249,plain,
% 1.20/1.41 (c0_1(a2218)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[444, 1247])).
% 1.20/1.41 tff(1250,plain,
% 1.20/1.41 (~c1_1(a2218)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[451, 150, 1249, 1248, 1245, 1220, 1244, 1243, 1219, 51, 1228])).
% 1.20/1.41 tff(1251,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[465, 150, 328, 72, 1249, 1248, 462, 1250])).
% 1.20/1.41 tff(1252,plain,(hskp34 | hskp33 | c0_1(a2181) | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1253,plain,
% 1.20/1.41 (hskp34),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1252, 99, 72, 97])).
% 1.20/1.41 tff(1254,plain,
% 1.20/1.41 (~c0_1(a2189)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[697, 1253])).
% 1.20/1.41 tff(1255,plain,
% 1.20/1.41 (c3_1(a2189)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[676, 1253])).
% 1.20/1.41 tff(1256,plain,
% 1.20/1.41 (c1_1(a2189)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[684, 1253])).
% 1.20/1.41 tff(1257,plain,
% 1.20/1.41 (~hskp18),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1241, 100, 99, 838, 97])).
% 1.20/1.41 tff(1258,plain,
% 1.20/1.41 (c3_1(a2181)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1217, 1257, 838])).
% 1.20/1.41 tff(1259,plain,
% 1.20/1.41 (~hskp48),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1165, 1258, 838, 99, 72])).
% 1.20/1.41 tff(1260,assumption,(hskp21), introduced(assumption)).
% 1.20/1.41 tff(1261,plain,
% 1.20/1.41 (((~hskp21) | (~c0_1(a2239))) <=> ((~hskp21) | (~c0_1(a2239)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1262,plain,
% 1.20/1.41 (((~c0_1(a2239)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a2239)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1263,axiom,((~c0_1(a2239)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.20/1.41 tff(1264,plain,
% 1.20/1.41 ((~hskp21) | (~c0_1(a2239))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 1.20/1.41 tff(1265,plain,
% 1.20/1.41 ((~hskp21) | (~c0_1(a2239))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1264, 1261])).
% 1.20/1.41 tff(1266,plain,
% 1.20/1.41 (~c0_1(a2239)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1265, 1260])).
% 1.20/1.41 tff(1267,assumption,(~c0_1(a2189)), introduced(assumption)).
% 1.20/1.41 tff(1268,plain,
% 1.20/1.41 (((~hskp21) | c2_1(a2239)) <=> ((~hskp21) | c2_1(a2239))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1269,axiom,((~hskp21) | c2_1(a2239)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 1.20/1.41 tff(1270,plain,
% 1.20/1.41 ((~hskp21) | c2_1(a2239)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 1.20/1.41 tff(1271,plain,
% 1.20/1.41 ((~hskp21) | c2_1(a2239)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1270, 1268])).
% 1.20/1.41 tff(1272,plain,
% 1.20/1.41 ((~hskp21) | c2_1(a2239)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1271, 1268])).
% 1.20/1.41 tff(1273,plain,
% 1.20/1.41 ((~hskp21) | c2_1(a2239)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1272, 1268])).
% 1.20/1.41 tff(1274,plain,
% 1.20/1.41 ((~hskp21) | c2_1(a2239)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1273, 1268])).
% 1.20/1.41 tff(1275,plain,
% 1.20/1.41 (c2_1(a2239)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1274, 1260])).
% 1.20/1.41 tff(1276,assumption,(c3_1(a2189)), introduced(assumption)).
% 1.20/1.41 tff(1277,assumption,(c1_1(a2189)), introduced(assumption)).
% 1.20/1.41 tff(1278,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1279,plain,
% 1.20/1.41 ((hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1280,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1279])).
% 1.20/1.41 tff(1281,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1280, 1278])).
% 1.20/1.41 tff(1282,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1283,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2239)) | (~c2_1(a2239))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 1.20/1.41 tff(1284,plain,
% 1.20/1.41 (~c1_1(a2239)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1283, 150, 1167, 1277, 1276, 1275, 1267, 1266, 41])).
% 1.20/1.41 tff(1285,assumption,(~hskp26), introduced(assumption)).
% 1.20/1.41 tff(1286,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1287,plain,
% 1.20/1.41 ((hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239))) <=> (hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1288,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1287])).
% 1.20/1.41 tff(1289,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1288, 1286])).
% 1.20/1.41 tff(1290,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1291,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2239) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | c1_1(a2239) | (~c2_1(a2239))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 1.20/1.41 tff(1292,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1291, 150, 1285, 1277, 1276, 1275, 1267, 1266, 1144, 1284])).
% 1.20/1.41 tff(1293,plain,((~hskp21) | hskp26 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189) | hskp48), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1294,plain,
% 1.20/1.41 (~hskp21),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1293, 1259, 1256, 1255, 1254, 1104])).
% 1.20/1.41 tff(1295,plain,
% 1.20/1.41 (hskp54),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[148, 1294, 1067])).
% 1.20/1.41 tff(1296,plain,
% 1.20/1.41 (((~hskp54) | c0_1(a2240)) <=> ((~hskp54) | c0_1(a2240))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1297,axiom,((~hskp54) | c0_1(a2240)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.20/1.41 tff(1298,plain,
% 1.20/1.41 ((~hskp54) | c0_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1297, 1296])).
% 1.20/1.41 tff(1299,plain,
% 1.20/1.41 ((~hskp54) | c0_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1298, 1296])).
% 1.20/1.41 tff(1300,plain,
% 1.20/1.41 ((~hskp54) | c0_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1299, 1296])).
% 1.20/1.41 tff(1301,plain,
% 1.20/1.41 ((~hskp54) | c0_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1300, 1296])).
% 1.20/1.41 tff(1302,plain,
% 1.20/1.41 ((~hskp54) | c0_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1301, 1296])).
% 1.20/1.41 tff(1303,plain,
% 1.20/1.41 (c0_1(a2240)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1302, 1295])).
% 1.20/1.41 tff(1304,plain,
% 1.20/1.41 (((~hskp54) | c1_1(a2240)) <=> ((~hskp54) | c1_1(a2240))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1305,axiom,((~hskp54) | c1_1(a2240)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.20/1.41 tff(1306,plain,
% 1.20/1.41 ((~hskp54) | c1_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.20/1.41 tff(1307,plain,
% 1.20/1.41 ((~hskp54) | c1_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1306, 1304])).
% 1.20/1.41 tff(1308,plain,
% 1.20/1.41 ((~hskp54) | c1_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1307, 1304])).
% 1.20/1.41 tff(1309,plain,
% 1.20/1.41 ((~hskp54) | c1_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1308, 1304])).
% 1.20/1.41 tff(1310,plain,
% 1.20/1.41 ((~hskp54) | c1_1(a2240)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1309, 1304])).
% 1.20/1.41 tff(1311,plain,
% 1.20/1.41 (c1_1(a2240)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1310, 1295])).
% 1.20/1.41 tff(1312,plain,
% 1.20/1.41 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1313,plain,
% 1.20/1.41 ((hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240))) <=> (hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1314,plain,
% 1.20/1.41 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1313])).
% 1.20/1.41 tff(1315,plain,
% 1.20/1.41 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1314, 1312])).
% 1.20/1.41 tff(1316,plain,
% 1.20/1.41 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2240)) | (~c0_1(a2240)) | (~c2_1(a2240)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1317,plain,
% 1.20/1.41 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | (~c2_1(a2240))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.20/1.41 tff(1318,plain,
% 1.20/1.41 (~c2_1(a2240)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1317, 150, 1085, 1311, 1303, 758])).
% 1.20/1.41 tff(1319,plain,
% 1.20/1.41 (~c2_1(a2189)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[718, 150, 72, 1256, 1255, 1254, 71])).
% 1.20/1.41 tff(1320,assumption,(hskp58), introduced(assumption)).
% 1.20/1.41 tff(1321,plain,
% 1.20/1.41 (~c1_1(a2252)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[163, 1320])).
% 1.20/1.41 tff(1322,plain,
% 1.20/1.41 (~c2_1(a2252)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[169, 1320])).
% 1.20/1.41 tff(1323,plain,
% 1.20/1.41 (c0_1(a2252)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[177, 1320])).
% 1.20/1.41 tff(1324,plain,
% 1.20/1.41 (~c3_1(a2252)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[919, 150, 100, 1323, 1322, 1321, 111])).
% 1.20/1.41 tff(1325,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1326,plain,
% 1.20/1.41 ((hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252))) <=> (hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1327,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1326])).
% 1.20/1.41 tff(1328,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1327, 1325])).
% 1.20/1.41 tff(1329,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1330,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2252) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2252) | (~c0_1(a2252))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 1.20/1.41 tff(1331,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1330, 150, 72, 1323, 1321, 99, 838, 97, 246, 1324])).
% 1.20/1.41 tff(1332,plain,((~hskp58) | hskp33 | c0_1(a2181) | c2_1(a2181) | hskp32), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1333,plain,
% 1.20/1.41 (~hskp58),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1332, 100, 99, 97, 72])).
% 1.20/1.41 tff(1334,assumption,(~hskp2), introduced(assumption)).
% 1.20/1.41 tff(1335,assumption,(~hskp58), introduced(assumption)).
% 1.20/1.41 tff(1336,plain,
% 1.20/1.41 (^[U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(1337,plain,
% 1.20/1.41 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[1336])).
% 1.20/1.41 tff(1338,plain,
% 1.20/1.41 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1339,plain,
% 1.20/1.41 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(1340,plain,
% 1.20/1.41 (![U: $i] : (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17) <=> ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[1339])).
% 1.20/1.41 tff(1341,axiom,(![U: $i] : (((((~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause255')).
% 1.20/1.41 tff(1342,plain,
% 1.20/1.41 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 1.20/1.41 tff(1343,plain,
% 1.20/1.41 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1342, 1338])).
% 1.20/1.41 tff(1344,plain,(
% 1.20/1.41 ![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.20/1.41 inference(skolemize,[status(sab)],[1343])).
% 1.20/1.41 tff(1345,plain,
% 1.20/1.41 (![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1344, 1337])).
% 1.20/1.41 tff(1346,assumption,(~c0_1(a2200)), introduced(assumption)).
% 1.20/1.41 tff(1347,assumption,(~c1_1(a2200)), introduced(assumption)).
% 1.20/1.41 tff(1348,plain,
% 1.20/1.41 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1349,plain,
% 1.20/1.41 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200)) <=> (hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1350,plain,
% 1.20/1.41 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200)))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1349])).
% 1.20/1.41 tff(1351,plain,
% 1.20/1.41 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1350, 1348])).
% 1.20/1.41 tff(1352,plain,
% 1.20/1.41 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2200) | c3_1(a2200) | c0_1(a2200))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1353,plain,
% 1.20/1.41 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c1_1(a2200) | c0_1(a2200) | (~ndr1_0) | c3_1(a2200)),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 1.20/1.41 tff(1354,plain,
% 1.20/1.41 (c1_1(a2200) | c3_1(a2200)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1353, 150, 100, 1334, 1346, 207])).
% 1.20/1.41 tff(1355,plain,
% 1.20/1.41 (c3_1(a2200)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1354, 1347])).
% 1.20/1.41 tff(1356,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1357,plain,
% 1.20/1.41 ((hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200))) <=> (hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1358,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1357])).
% 1.20/1.41 tff(1359,plain,
% 1.20/1.41 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1358, 1356])).
% 1.20/1.41 tff(1360,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2200) | c1_1(a2200) | (~c2_1(a2200)))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1361,plain,
% 1.20/1.41 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c1_1(a2200) | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.20/1.41 tff(1362,plain,
% 1.20/1.41 (c1_1(a2200) | (~c2_1(a2200))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1361, 150, 1285, 1277, 1276, 1346, 1267, 1144])).
% 1.20/1.41 tff(1363,plain,
% 1.20/1.41 (~c2_1(a2200)),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1362, 1347])).
% 1.20/1.41 tff(1364,plain,
% 1.20/1.41 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1365,plain,
% 1.20/1.41 ((hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200))) <=> (hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1366,plain,
% 1.20/1.41 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1365])).
% 1.20/1.41 tff(1367,plain,
% 1.20/1.41 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1366, 1364])).
% 1.20/1.42 tff(1368,plain,
% 1.20/1.42 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2200) | c1_1(a2200) | (~c3_1(a2200)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1369,plain,
% 1.20/1.42 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c1_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c3_1(a2200))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 1.20/1.42 tff(1370,plain,
% 1.20/1.42 ($false),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1369, 1335, 150, 1347, 1363, 121, 1355])).
% 1.20/1.42 tff(1371,plain,(c1_1(a2200) | hskp58 | hskp32 | hskp2 | c0_1(a2200) | hskp26 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.42 tff(1372,plain,
% 1.20/1.42 (c1_1(a2200)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1371, 1346, 100, 1334, 1335, 1285, 1277, 1276, 1267])).
% 1.20/1.42 tff(1373,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1374,plain,
% 1.20/1.42 ((hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1375,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1374])).
% 1.20/1.42 tff(1376,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1375, 1373])).
% 1.20/1.42 tff(1377,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1378,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2200) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2200))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1377, 1376])).
% 1.20/1.42 tff(1379,plain,
% 1.20/1.42 ((~c2_1(a2200)) | (~c1_1(a2200))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1378, 150, 1167, 1277, 1276, 1346, 1267, 41])).
% 1.20/1.42 tff(1380,plain,
% 1.20/1.42 (~c2_1(a2200)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1379, 1372])).
% 1.20/1.42 tff(1381,assumption,(~hskp18), introduced(assumption)).
% 1.20/1.42 tff(1382,plain,
% 1.20/1.42 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1383,plain,
% 1.20/1.42 ((hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200))) <=> (hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1384,plain,
% 1.20/1.42 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200)))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1383])).
% 1.20/1.42 tff(1385,plain,
% 1.20/1.42 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1384, 1382])).
% 1.20/1.42 tff(1386,plain,
% 1.20/1.42 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2200) | c3_1(a2200) | (~c1_1(a2200)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1387,plain,
% 1.20/1.42 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2200) | (~ndr1_0) | (~c1_1(a2200)) | c3_1(a2200)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.20/1.42 tff(1388,plain,
% 1.20/1.42 (c3_1(a2200)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1387, 150, 1381, 1372, 1380, 61])).
% 1.20/1.42 tff(1389,assumption,(hskp54), introduced(assumption)).
% 1.20/1.42 tff(1390,plain,
% 1.20/1.42 (c0_1(a2240)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1302, 1389])).
% 1.20/1.42 tff(1391,plain,
% 1.20/1.42 (c1_1(a2240)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1310, 1389])).
% 1.20/1.42 tff(1392,plain,
% 1.20/1.42 (~c2_1(a2240)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1317, 150, 759, 1391, 1390, 758])).
% 1.20/1.42 tff(1393,assumption,(c3_1(a2200)), introduced(assumption)).
% 1.20/1.42 tff(1394,assumption,(~c2_1(a2200)), introduced(assumption)).
% 1.20/1.42 tff(1395,assumption,(c1_1(a2200)), introduced(assumption)).
% 1.20/1.42 tff(1396,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1397,plain,
% 1.20/1.42 (((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200))) <=> (c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1398,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1397])).
% 1.20/1.42 tff(1399,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1398, 1396])).
% 1.20/1.42 tff(1400,plain,
% 1.20/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2200) | c2_1(a2200) | (~c1_1(a2200)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1401,plain,
% 1.20/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2200) | c2_1(a2200) | (~ndr1_0) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240) | (~c1_1(a2200)) | (~c3_1(a2200))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 1.20/1.42 tff(1402,plain,
% 1.20/1.42 ($false),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1401, 150, 1391, 1390, 1395, 1346, 1394, 339, 1393, 1392])).
% 1.20/1.42 tff(1403,plain,((~hskp54) | (~c1_1(a2200)) | c0_1(a2200) | c2_1(a2200) | (~c3_1(a2200)) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.20/1.42 tff(1404,plain,
% 1.20/1.42 (~hskp54),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1403, 1372, 1346, 1380, 1388, 759])).
% 1.20/1.42 tff(1405,plain,
% 1.20/1.42 (hskp21),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[148, 1404, 1067])).
% 1.20/1.42 tff(1406,plain,
% 1.20/1.42 (((~hskp21) | (~c3_1(a2239))) <=> ((~hskp21) | (~c3_1(a2239)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1407,plain,
% 1.20/1.42 (((~c3_1(a2239)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a2239)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1408,axiom,((~c3_1(a2239)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.20/1.42 tff(1409,plain,
% 1.20/1.42 ((~hskp21) | (~c3_1(a2239))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 1.20/1.42 tff(1410,plain,
% 1.20/1.42 ((~hskp21) | (~c3_1(a2239))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1409, 1406])).
% 1.20/1.42 tff(1411,plain,
% 1.20/1.42 (~c3_1(a2239)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1410, 1405])).
% 1.20/1.42 tff(1412,plain,
% 1.20/1.42 (c2_1(a2239)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1274, 1405])).
% 1.20/1.42 tff(1413,assumption,(hskp17), introduced(assumption)).
% 1.20/1.42 tff(1414,plain,
% 1.20/1.42 (((~hskp17) | (~c3_1(a2221))) <=> ((~hskp17) | (~c3_1(a2221)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1415,plain,
% 1.20/1.42 (((~c3_1(a2221)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a2221)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1416,axiom,((~c3_1(a2221)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 1.20/1.42 tff(1417,plain,
% 1.20/1.42 ((~hskp17) | (~c3_1(a2221))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 1.20/1.42 tff(1418,plain,
% 1.20/1.42 ((~hskp17) | (~c3_1(a2221))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1417, 1414])).
% 1.20/1.42 tff(1419,plain,
% 1.20/1.42 (~c3_1(a2221)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1418, 1413])).
% 1.20/1.42 tff(1420,plain,
% 1.20/1.42 (((~hskp17) | (~c0_1(a2221))) <=> ((~hskp17) | (~c0_1(a2221)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1421,plain,
% 1.20/1.42 (((~c0_1(a2221)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a2221)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1422,axiom,((~c0_1(a2221)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause204')).
% 1.20/1.42 tff(1423,plain,
% 1.20/1.42 ((~hskp17) | (~c0_1(a2221))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.20/1.42 tff(1424,plain,
% 1.20/1.42 ((~hskp17) | (~c0_1(a2221))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1423, 1420])).
% 1.20/1.42 tff(1425,plain,
% 1.20/1.42 (~c0_1(a2221)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1424, 1413])).
% 1.20/1.42 tff(1426,plain,
% 1.20/1.42 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1427,plain,
% 1.20/1.42 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221)) <=> (hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1428,plain,
% 1.20/1.42 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221)))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1427])).
% 1.20/1.42 tff(1429,plain,
% 1.20/1.42 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1428, 1426])).
% 1.20/1.42 tff(1430,plain,
% 1.20/1.42 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2221) | c3_1(a2221) | c0_1(a2221))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1431,plain,
% 1.20/1.42 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | c1_1(a2221)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.20/1.42 tff(1432,plain,
% 1.20/1.42 (c1_1(a2221)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1431, 150, 100, 1334, 1425, 1419, 207])).
% 1.20/1.42 tff(1433,plain,
% 1.20/1.42 (((~hskp17) | c2_1(a2221)) <=> ((~hskp17) | c2_1(a2221))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1434,axiom,((~hskp17) | c2_1(a2221)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.20/1.42 tff(1435,plain,
% 1.20/1.42 ((~hskp17) | c2_1(a2221)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1434, 1433])).
% 1.20/1.42 tff(1436,plain,
% 1.20/1.42 ((~hskp17) | c2_1(a2221)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1435, 1433])).
% 1.20/1.42 tff(1437,plain,
% 1.20/1.42 ((~hskp17) | c2_1(a2221)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1436, 1433])).
% 1.20/1.42 tff(1438,plain,
% 1.20/1.42 ((~hskp17) | c2_1(a2221)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1437, 1433])).
% 1.20/1.42 tff(1439,plain,
% 1.20/1.42 ((~hskp17) | c2_1(a2221)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1438, 1433])).
% 1.20/1.42 tff(1440,plain,
% 1.20/1.42 (c2_1(a2221)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1439, 1413])).
% 1.20/1.42 tff(1441,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1442,plain,
% 1.20/1.42 ((hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1443,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1442])).
% 1.20/1.42 tff(1444,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1443, 1441])).
% 1.20/1.42 tff(1445,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2221) | (~c1_1(a2221)) | (~c2_1(a2221)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1446,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2221) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c1_1(a2221)) | (~c2_1(a2221))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 1.20/1.42 tff(1447,plain,
% 1.20/1.42 ($false),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1446, 150, 1167, 1277, 1276, 1440, 1267, 1425, 41, 1432])).
% 1.20/1.42 tff(1448,plain,((~hskp17) | hskp48 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189) | hskp32 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.20/1.42 tff(1449,plain,
% 1.20/1.42 (~hskp17),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1448, 1334, 1277, 1276, 1267, 100, 1167])).
% 1.20/1.42 tff(1450,plain,
% 1.20/1.42 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1451,plain,
% 1.20/1.42 ((hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239))) <=> (hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1452,plain,
% 1.20/1.42 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1451])).
% 1.20/1.42 tff(1453,plain,
% 1.20/1.42 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1452, 1450])).
% 1.20/1.42 tff(1454,plain,
% 1.20/1.42 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2239) | (~c1_1(a2239)) | (~c2_1(a2239)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1455,plain,
% 1.20/1.42 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | c3_1(a2239) | (~ndr1_0) | (~c1_1(a2239)) | (~c2_1(a2239))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 1.20/1.42 tff(1456,plain,
% 1.20/1.42 (~c1_1(a2239)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1455, 150, 1449, 1412, 1411, 1345])).
% 1.20/1.42 tff(1457,plain,
% 1.20/1.42 (~c0_1(a2239)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1265, 1405])).
% 1.20/1.42 tff(1458,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1459,plain,
% 1.20/1.42 ((hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239))) <=> (hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1460,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1459])).
% 1.20/1.42 tff(1461,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1460, 1458])).
% 1.20/1.42 tff(1462,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2200) | (~c1_1(a2200)) | (~c3_1(a2200)) | c0_1(a2239) | c1_1(a2239) | (~c2_1(a2239)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1463,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2200) | c0_1(a2239) | (~ndr1_0) | c1_1(a2239) | (~c2_1(a2239)) | (~c1_1(a2200)) | (~c3_1(a2200))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 1.20/1.42 tff(1464,plain,
% 1.20/1.42 ($false),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1463, 150, 1285, 1372, 1412, 1346, 1457, 1144, 1388, 1456])).
% 1.20/1.42 tff(1465,plain,(c0_1(a2200) | hskp26 | hskp0 | hskp18 | hskp48 | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2189) | hskp32 | hskp2 | hskp58), inference(lemma,lemma(discharge,[]))).
% 1.20/1.42 tff(1466,plain,
% 1.20/1.42 (c0_1(a2200)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1465, 1335, 1085, 1257, 1259, 1256, 1255, 1254, 100, 1334, 1285])).
% 1.20/1.42 tff(1467,assumption,(c0_1(a2200)), introduced(assumption)).
% 1.20/1.42 tff(1468,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1469,plain,
% 1.20/1.42 (((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> ((~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1470,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1469])).
% 1.20/1.42 tff(1471,plain,
% 1.20/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200)))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1470, 1468])).
% 1.20/1.42 tff(1472,plain,
% 1.20/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2181) | (~c1_1(a2181)) | (~c3_1(a2181)) | c2_1(a2200) | (~c0_1(a2200)) | (~c1_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1473,plain,
% 1.20/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (~c0_1(a2200)) | c2_1(a2200) | c0_1(a2189) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c1_1(a2189)) | (~c1_1(a2200))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 1.20/1.42 tff(1474,plain,
% 1.20/1.42 (~c1_1(a2200)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1473, 150, 1256, 1467, 1394, 1254, 838, 97, 339, 101, 1319])).
% 1.20/1.42 tff(1475,plain,
% 1.20/1.42 (~c3_1(a2200)),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1369, 1335, 150, 1474, 1394, 121])).
% 1.20/1.42 tff(1476,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1477,plain,
% 1.20/1.42 ((hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200))) <=> (hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1478,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200)))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1477])).
% 1.20/1.42 tff(1479,plain,
% 1.20/1.42 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.20/1.42 tff(1480,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp33 | (~ndr1_0) | c2_1(a2181) | c0_1(a2181) | (~c1_1(a2181)) | c1_1(a2200) | c3_1(a2200) | (~c0_1(a2200)))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1481,plain,
% 1.20/1.42 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp33 | c1_1(a2200) | (~c0_1(a2200)) | c0_1(a2181) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c3_1(a2200)),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.20/1.42 tff(1482,plain,
% 1.20/1.42 ($false),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1481, 150, 72, 1474, 1467, 99, 838, 97, 246, 1475])).
% 1.20/1.42 tff(1483,plain,(c2_1(a2200) | hskp33 | (~c0_1(a2200)) | c0_1(a2181) | c2_1(a2181) | hskp58 | (~c3_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.43 tff(1484,plain,
% 1.20/1.43 (c2_1(a2200)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1483, 1466, 72, 99, 97, 1335, 1258])).
% 1.20/1.43 tff(1485,plain,
% 1.20/1.43 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1486,plain,
% 1.20/1.43 ((hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200))) <=> (hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1487,plain,
% 1.20/1.43 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200))))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1486])).
% 1.20/1.43 tff(1488,plain,
% 1.20/1.43 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200)))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1487, 1485])).
% 1.20/1.43 tff(1489,plain,
% 1.20/1.43 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1490,plain,
% 1.20/1.43 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2200)) | (~c2_1(a2200)) | (~ndr1_0) | (~c1_1(a2200))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 1.20/1.43 tff(1491,plain,
% 1.20/1.43 ((~c2_1(a2200)) | (~c1_1(a2200))),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1490, 150, 1085, 1466, 758])).
% 1.20/1.43 tff(1492,plain,
% 1.20/1.43 (~c1_1(a2200)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1491, 1484])).
% 1.20/1.43 tff(1493,plain,
% 1.20/1.43 (c3_1(a2200)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1481, 150, 72, 1492, 1466, 99, 838, 97, 246])).
% 1.20/1.43 tff(1494,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1495,plain,
% 1.20/1.43 (((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189))) <=> ((~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1496,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200))))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1495])).
% 1.20/1.43 tff(1497,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200)))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1496, 1494])).
% 1.20/1.43 tff(1498,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2200)) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1499,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (~c0_1(a2200)) | (~c2_1(a2200)) | c0_1(a2189) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c3_1(a2200))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 1.20/1.43 tff(1500,plain,
% 1.20/1.43 ($false),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1499, 150, 1256, 1255, 1466, 1484, 1254, 302, 1319, 1493])).
% 1.20/1.43 tff(1501,plain,(hskp58 | hskp33 | c0_1(a2181) | c2_1(a2181) | hskp32 | hskp2 | hskp26), inference(lemma,lemma(discharge,[]))).
% 1.20/1.43 tff(1502,plain,
% 1.20/1.43 (hskp2),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1501, 100, 99, 97, 1104, 72, 1333])).
% 1.20/1.43 tff(1503,plain,
% 1.20/1.43 (~c2_1(a2187)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[220, 1502])).
% 1.20/1.43 tff(1504,plain,
% 1.20/1.43 (c1_1(a2187)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[276, 1502])).
% 1.20/1.43 tff(1505,plain,
% 1.20/1.43 (c3_1(a2187)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[228, 1502])).
% 1.20/1.43 tff(1506,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1507,plain,
% 1.20/1.43 (((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> (c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1508,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240)))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1507])).
% 1.20/1.43 tff(1509,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1508, 1506])).
% 1.20/1.43 tff(1510,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2240) | (~c0_1(a2240)) | (~c1_1(a2240)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1511,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c2_1(a2189) | (~c1_1(a2189)) | (~c0_1(a2240)) | (~c1_1(a2240)) | c2_1(a2240)),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.20/1.43 tff(1512,plain,
% 1.20/1.43 ($false),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1511, 150, 1311, 1303, 1256, 1505, 1504, 1254, 1503, 339, 1319, 1318])).
% 1.20/1.43 tff(1513,plain,(hskp32 | c0_1(a2181) | hskp33 | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.43 tff(1514,plain,
% 1.20/1.43 (hskp32),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1513, 99, 72, 97])).
% 1.20/1.43 tff(1515,plain,
% 1.20/1.43 (c0_1(a2186)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[80, 1514])).
% 1.20/1.43 tff(1516,plain,
% 1.20/1.43 (~c3_1(a2186)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[86, 1514])).
% 1.20/1.43 tff(1517,plain,
% 1.20/1.43 (~c2_1(a2186)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[324, 1514])).
% 1.20/1.43 tff(1518,plain,
% 1.20/1.43 (~c1_1(a2186)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[725, 150, 1256, 1255, 1515, 1254, 1517, 339, 1319])).
% 1.20/1.43 tff(1519,plain,
% 1.20/1.43 (hskp53),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[491, 1518, 1517, 1516, 1515])).
% 1.20/1.43 tff(1520,plain,
% 1.20/1.43 (c0_1(a2235)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[95, 1519])).
% 1.20/1.43 tff(1521,plain,
% 1.20/1.43 (c2_1(a2235)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[619, 1519])).
% 1.20/1.43 tff(1522,plain,
% 1.20/1.43 (c3_1(a2235)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[627, 1519])).
% 1.20/1.43 tff(1523,plain,
% 1.20/1.43 ($false),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[737, 1522, 1521, 72, 1253, 1520])).
% 1.20/1.43 tff(1524,plain,(c0_1(a2181) | hskp33 | c2_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.43 tff(1525,plain,
% 1.20/1.43 (c0_1(a2181)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1524, 97, 72])).
% 1.20/1.43 tff(1526,assumption,(c0_1(a2181)), introduced(assumption)).
% 1.20/1.43 tff(1527,plain,
% 1.20/1.43 (c3_1(a2181)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1217, 1381, 1145])).
% 1.20/1.43 tff(1528,plain,
% 1.20/1.43 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.20/1.43 inference(bind,[status(th)],[])).
% 1.20/1.43 tff(1529,plain,
% 1.20/1.43 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.20/1.43 inference(quant_intro,[status(thm)],[1528])).
% 1.20/1.43 tff(1530,plain,
% 1.20/1.43 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1531,plain,
% 1.20/1.43 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.20/1.43 inference(bind,[status(th)],[])).
% 1.20/1.43 tff(1532,plain,
% 1.20/1.43 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.20/1.43 inference(quant_intro,[status(thm)],[1531])).
% 1.20/1.43 tff(1533,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause281')).
% 1.20/1.43 tff(1534,plain,
% 1.20/1.43 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.20/1.43 tff(1535,plain,
% 1.20/1.43 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1534, 1530])).
% 1.20/1.43 tff(1536,plain,(
% 1.20/1.43 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.20/1.43 inference(skolemize,[status(sab)],[1535])).
% 1.20/1.43 tff(1537,plain,
% 1.20/1.43 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1536, 1529])).
% 1.20/1.43 tff(1538,plain,
% 1.20/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1539,plain,
% 1.20/1.43 ((hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181))) <=> (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1540,plain,
% 1.20/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1539])).
% 1.20/1.43 tff(1541,plain,
% 1.20/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1540, 1538])).
% 1.20/1.43 tff(1542,plain,
% 1.20/1.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c2_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1543,plain,
% 1.20/1.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 1.20/1.43 tff(1544,plain,
% 1.20/1.43 (hskp10 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c3_1(a2181))),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1543, 150, 97, 1537])).
% 1.20/1.43 tff(1545,plain,
% 1.20/1.43 (hskp10),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1544, 1527, 1145, 1526])).
% 1.20/1.43 tff(1546,plain,
% 1.20/1.43 (((~hskp10) | (~c3_1(a2206))) <=> ((~hskp10) | (~c3_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1547,plain,
% 1.20/1.43 (((~c3_1(a2206)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1548,axiom,((~c3_1(a2206)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause220')).
% 1.20/1.43 tff(1549,plain,
% 1.20/1.43 ((~hskp10) | (~c3_1(a2206))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 1.20/1.43 tff(1550,plain,
% 1.20/1.43 ((~hskp10) | (~c3_1(a2206))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1549, 1546])).
% 1.20/1.43 tff(1551,plain,
% 1.20/1.43 (~c3_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1550, 1545])).
% 1.20/1.43 tff(1552,plain,
% 1.20/1.43 (((~hskp10) | (~c2_1(a2206))) <=> ((~hskp10) | (~c2_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1553,plain,
% 1.20/1.43 (((~c2_1(a2206)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1554,axiom,((~c2_1(a2206)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause218')).
% 1.20/1.43 tff(1555,plain,
% 1.20/1.43 ((~hskp10) | (~c2_1(a2206))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.20/1.43 tff(1556,plain,
% 1.20/1.43 ((~hskp10) | (~c2_1(a2206))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1555, 1552])).
% 1.20/1.43 tff(1557,plain,
% 1.20/1.43 (~c2_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1556, 1545])).
% 1.20/1.43 tff(1558,plain,
% 1.20/1.43 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1559,plain,
% 1.20/1.43 ((hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206))) <=> (hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1560,plain,
% 1.20/1.43 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206))))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1559])).
% 1.20/1.43 tff(1561,plain,
% 1.20/1.43 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206)))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1560, 1558])).
% 1.20/1.43 tff(1562,plain,
% 1.20/1.43 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1563,plain,
% 1.20/1.43 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c2_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c1_1(a2206))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 1.20/1.43 tff(1564,plain,
% 1.20/1.43 (~c1_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1563, 150, 1381, 1557, 1551, 61])).
% 1.20/1.43 tff(1565,plain,
% 1.20/1.43 (((~hskp10) | (~c0_1(a2206))) <=> ((~hskp10) | (~c0_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1566,plain,
% 1.20/1.43 (((~c0_1(a2206)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a2206)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1567,axiom,((~c0_1(a2206)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause219')).
% 1.20/1.43 tff(1568,plain,
% 1.20/1.43 ((~hskp10) | (~c0_1(a2206))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1567, 1566])).
% 1.20/1.43 tff(1569,plain,
% 1.20/1.43 ((~hskp10) | (~c0_1(a2206))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1568, 1565])).
% 1.20/1.43 tff(1570,plain,
% 1.20/1.43 (~c0_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1569, 1545])).
% 1.20/1.43 tff(1571,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1572,plain,
% 1.20/1.43 (((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206)) <=> (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1573,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206)))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1572])).
% 1.20/1.43 tff(1574,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1573, 1571])).
% 1.20/1.43 tff(1575,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2181) | (~c3_1(a2181)) | (~c0_1(a2181)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1576,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~c0_1(a2181)) | c2_1(a2181) | (~ndr1_0) | (~c3_1(a2181)) | c1_1(a2206)),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 1.20/1.43 tff(1577,plain,
% 1.20/1.43 ($false),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1576, 150, 1557, 1570, 1551, 1526, 97, 197, 1527, 1564])).
% 1.20/1.43 tff(1578,plain,(hskp18 | (~c0_1(a2181)) | c2_1(a2181) | (~c1_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.43 tff(1579,plain,
% 1.20/1.43 (hskp18),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1578, 1525, 97, 838])).
% 1.20/1.43 tff(1580,plain,
% 1.20/1.43 (c0_1(a2222)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[423, 1579])).
% 1.20/1.43 tff(1581,plain,
% 1.20/1.43 (c3_1(a2222)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[390, 1579])).
% 1.20/1.43 tff(1582,plain,
% 1.20/1.43 (~c2_1(a2222)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[352, 1579])).
% 1.20/1.43 tff(1583,assumption,(c1_1(a2222)), introduced(assumption)).
% 1.20/1.43 tff(1584,assumption,(~c2_1(a2222)), introduced(assumption)).
% 1.20/1.43 tff(1585,assumption,(c3_1(a2222)), introduced(assumption)).
% 1.20/1.43 tff(1586,assumption,(c0_1(a2222)), introduced(assumption)).
% 1.20/1.43 tff(1587,plain,
% 1.20/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1588,plain,
% 1.20/1.43 ((hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222))) <=> (hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1589,plain,
% 1.20/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1588])).
% 1.20/1.43 tff(1590,plain,
% 1.20/1.43 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1589, 1587])).
% 1.20/1.43 tff(1591,plain,
% 1.20/1.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c3_1(a2222)) | (~c1_1(a2222)))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1592,plain,
% 1.20/1.43 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2222) | (~ndr1_0) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 1.20/1.43 tff(1593,plain,
% 1.20/1.43 (hskp10 | (~c1_1(a2222))),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1592, 150, 1586, 1585, 1584, 1537])).
% 1.20/1.43 tff(1594,plain,
% 1.20/1.43 (hskp10),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1593, 1583])).
% 1.20/1.43 tff(1595,plain,
% 1.20/1.43 (~c3_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1550, 1594])).
% 1.20/1.43 tff(1596,plain,
% 1.20/1.43 (~c0_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1569, 1594])).
% 1.20/1.43 tff(1597,plain,
% 1.20/1.43 (~c2_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1556, 1594])).
% 1.20/1.43 tff(1598,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1599,plain,
% 1.20/1.43 (((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206)) <=> (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1600,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 1.20/1.43 inference(monotonicity,[status(thm)],[1599])).
% 1.20/1.43 tff(1601,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.43 inference(transitivity,[status(thm)],[1600, 1598])).
% 1.20/1.43 tff(1602,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))),
% 1.20/1.43 inference(quant_inst,[status(thm)],[])).
% 1.20/1.43 tff(1603,plain,
% 1.20/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 1.20/1.43 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.20/1.43 tff(1604,plain,
% 1.20/1.43 (c1_1(a2206)),
% 1.20/1.43 inference(unit_resolution,[status(thm)],[1603, 150, 1586, 1585, 1584, 1597, 1596, 1595, 197])).
% 1.20/1.43 tff(1605,plain,
% 1.20/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.43 inference(rewrite,[status(thm)],[])).
% 1.20/1.43 tff(1606,plain,
% 1.20/1.43 (((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206))) <=> (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1607,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 1.20/1.44 inference(monotonicity,[status(thm)],[1606])).
% 1.20/1.44 tff(1608,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.44 inference(transitivity,[status(thm)],[1607, 1605])).
% 1.20/1.44 tff(1609,plain,
% 1.20/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2222) | (~c1_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c1_1(a2222)) | c0_1(a2206) | c2_1(a2206) | (~c1_1(a2206)))),
% 1.20/1.44 inference(quant_inst,[status(thm)],[])).
% 1.20/1.44 tff(1610,plain,
% 1.20/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | (~ndr1_0) | (~c1_1(a2206)) | (~c1_1(a2222)) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.20/1.44 tff(1611,plain,
% 1.20/1.44 ($false),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1610, 150, 1586, 1585, 1584, 1597, 1596, 339, 1583, 1604])).
% 1.20/1.44 tff(1612,plain,((~c1_1(a2222)) | (~c0_1(a2222)) | (~c3_1(a2222)) | c2_1(a2222)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.44 tff(1613,plain,
% 1.20/1.44 (~c1_1(a2222)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1612, 1582, 1581, 1580])).
% 1.20/1.44 tff(1614,plain,
% 1.20/1.44 (^[V: $i, U: $i] : refl((hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))),
% 1.20/1.44 inference(bind,[status(th)],[])).
% 1.20/1.44 tff(1615,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.20/1.44 inference(quant_intro,[status(thm)],[1614])).
% 1.20/1.44 tff(1616,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1617,plain,
% 1.20/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp44))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V))) | hskp44) <=> (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44) <=> (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))))),
% 1.20/1.44 inference(bind,[status(th)],[])).
% 1.20/1.44 tff(1618,plain,
% 1.20/1.44 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44) <=> ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.20/1.44 inference(quant_intro,[status(thm)],[1617])).
% 1.20/1.44 tff(1619,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c2_1(V)) | hskp44)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause278')).
% 1.20/1.44 tff(1620,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1619, 1618])).
% 1.20/1.44 tff(1621,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1620, 1616])).
% 1.20/1.44 tff(1622,plain,(
% 1.20/1.44 ![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.20/1.44 inference(skolemize,[status(sab)],[1621])).
% 1.20/1.44 tff(1623,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1622, 1615])).
% 1.20/1.44 tff(1624,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1625,plain,
% 1.20/1.44 ((hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222))) <=> (hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1626,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))))),
% 1.20/1.44 inference(monotonicity,[status(thm)],[1625])).
% 1.20/1.44 tff(1627,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222)))) <=> ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)))),
% 1.20/1.44 inference(transitivity,[status(thm)],[1626, 1624])).
% 1.20/1.44 tff(1628,plain,
% 1.20/1.44 ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp44 | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c2_1(a2222) | (~c0_1(a2222)) | (~c3_1(a2222)))),
% 1.20/1.44 inference(quant_inst,[status(thm)],[])).
% 1.20/1.44 tff(1629,plain,
% 1.20/1.44 ((~![V: $i, U: $i] : (hskp44 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp44 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.20/1.44 tff(1630,plain,
% 1.20/1.44 (hskp44),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1629, 150, 1580, 1581, 1582, 1623, 1613])).
% 1.20/1.44 tff(1631,plain,
% 1.20/1.44 (((~hskp44) | (~c0_1(a2215))) <=> ((~hskp44) | (~c0_1(a2215)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1632,plain,
% 1.20/1.44 (((~c0_1(a2215)) | (~hskp44)) <=> ((~hskp44) | (~c0_1(a2215)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1633,axiom,((~c0_1(a2215)) | (~hskp44)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.20/1.44 tff(1634,plain,
% 1.20/1.44 ((~hskp44) | (~c0_1(a2215))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1633, 1632])).
% 1.20/1.44 tff(1635,plain,
% 1.20/1.44 ((~hskp44) | (~c0_1(a2215))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1634, 1631])).
% 1.20/1.44 tff(1636,plain,
% 1.20/1.44 (~c0_1(a2215)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1635, 1630])).
% 1.20/1.44 tff(1637,plain,
% 1.20/1.44 (((~hskp44) | c1_1(a2215)) <=> ((~hskp44) | c1_1(a2215))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1638,axiom,((~hskp44) | c1_1(a2215)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.20/1.44 tff(1639,plain,
% 1.20/1.44 ((~hskp44) | c1_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.20/1.44 tff(1640,plain,
% 1.20/1.44 ((~hskp44) | c1_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1639, 1637])).
% 1.20/1.44 tff(1641,plain,
% 1.20/1.44 ((~hskp44) | c1_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1640, 1637])).
% 1.20/1.44 tff(1642,plain,
% 1.20/1.44 ((~hskp44) | c1_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1641, 1637])).
% 1.20/1.44 tff(1643,plain,
% 1.20/1.44 ((~hskp44) | c1_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1642, 1637])).
% 1.20/1.44 tff(1644,plain,
% 1.20/1.44 (c1_1(a2215)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1643, 1630])).
% 1.20/1.44 tff(1645,plain,
% 1.20/1.44 (((~hskp44) | c2_1(a2215)) <=> ((~hskp44) | c2_1(a2215))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1646,axiom,((~hskp44) | c2_1(a2215)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.20/1.44 tff(1647,plain,
% 1.20/1.44 ((~hskp44) | c2_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1646, 1645])).
% 1.20/1.44 tff(1648,plain,
% 1.20/1.44 ((~hskp44) | c2_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1647, 1645])).
% 1.20/1.44 tff(1649,plain,
% 1.20/1.44 ((~hskp44) | c2_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1648, 1645])).
% 1.20/1.44 tff(1650,plain,
% 1.20/1.44 ((~hskp44) | c2_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1649, 1645])).
% 1.20/1.44 tff(1651,plain,
% 1.20/1.44 ((~hskp44) | c2_1(a2215)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1650, 1645])).
% 1.20/1.44 tff(1652,plain,
% 1.20/1.44 (c2_1(a2215)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1651, 1630])).
% 1.20/1.44 tff(1653,plain,
% 1.20/1.44 (~c1_1(a2222)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1612, 1232, 1231, 1230])).
% 1.20/1.44 tff(1654,plain,
% 1.20/1.44 ($false),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1239, 150, 100, 1232, 1231, 1230, 111, 1653])).
% 1.20/1.44 tff(1655,plain,((~hskp18) | hskp32), inference(lemma,lemma(discharge,[]))).
% 1.20/1.44 tff(1656,plain,
% 1.20/1.44 (hskp32),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1655, 1579])).
% 1.20/1.44 tff(1657,plain,
% 1.20/1.44 (~c2_1(a2186)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[324, 1656])).
% 1.20/1.44 tff(1658,plain,
% 1.20/1.44 (~c3_1(a2186)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[86, 1656])).
% 1.20/1.44 tff(1659,plain,
% 1.20/1.44 (c0_1(a2186)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[80, 1656])).
% 1.20/1.44 tff(1660,plain,
% 1.20/1.44 (~hskp53),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[767, 328, 759, 72])).
% 1.20/1.44 tff(1661,plain,
% 1.20/1.44 (c1_1(a2186)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[491, 1660, 480, 481, 482])).
% 1.20/1.44 tff(1662,plain,
% 1.20/1.44 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.20/1.44 inference(bind,[status(th)],[])).
% 1.20/1.44 tff(1663,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.20/1.44 inference(quant_intro,[status(thm)],[1662])).
% 1.20/1.44 tff(1664,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1665,plain,
% 1.20/1.44 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.20/1.44 inference(bind,[status(th)],[])).
% 1.20/1.44 tff(1666,plain,
% 1.20/1.44 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.20/1.44 inference(quant_intro,[status(thm)],[1665])).
% 1.20/1.44 tff(1667,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause274')).
% 1.20/1.44 tff(1668,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 1.20/1.44 tff(1669,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1668, 1664])).
% 1.20/1.44 tff(1670,plain,(
% 1.20/1.44 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.20/1.44 inference(skolemize,[status(sab)],[1669])).
% 1.20/1.44 tff(1671,plain,
% 1.20/1.44 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1670, 1663])).
% 1.20/1.44 tff(1672,assumption,(~c0_1(a2215)), introduced(assumption)).
% 1.20/1.44 tff(1673,assumption,(c1_1(a2215)), introduced(assumption)).
% 1.20/1.44 tff(1674,assumption,(c2_1(a2215)), introduced(assumption)).
% 1.20/1.44 tff(1675,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1676,plain,
% 1.20/1.44 ((hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215))) <=> (hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1677,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215))))),
% 1.20/1.44 inference(monotonicity,[status(thm)],[1676])).
% 1.20/1.44 tff(1678,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.20/1.44 inference(transitivity,[status(thm)],[1677, 1675])).
% 1.20/1.44 tff(1679,plain,
% 1.20/1.44 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c1_1(a2186)) | c0_1(a2215) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.20/1.44 inference(quant_inst,[status(thm)],[])).
% 1.20/1.44 tff(1680,plain,
% 1.20/1.44 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c0_1(a2215) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c1_1(a2186)) | (~c2_1(a2215)) | (~c1_1(a2215))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 1.20/1.44 tff(1681,plain,
% 1.20/1.44 (hskp4 | (~c1_1(a2186))),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1680, 150, 1674, 1673, 1672, 481, 480, 1671])).
% 1.20/1.44 tff(1682,plain,
% 1.20/1.44 (hskp4),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1681, 1661])).
% 1.20/1.44 tff(1683,plain,
% 1.20/1.44 (((~hskp4) | (~c1_1(a2191))) <=> ((~hskp4) | (~c1_1(a2191)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1684,plain,
% 1.20/1.44 (((~c1_1(a2191)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a2191)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1685,axiom,((~c1_1(a2191)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause233')).
% 1.20/1.44 tff(1686,plain,
% 1.20/1.44 ((~hskp4) | (~c1_1(a2191))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.20/1.44 tff(1687,plain,
% 1.20/1.44 ((~hskp4) | (~c1_1(a2191))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1686, 1683])).
% 1.20/1.44 tff(1688,plain,
% 1.20/1.44 (~c1_1(a2191)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1687, 1682])).
% 1.20/1.44 tff(1689,plain,
% 1.20/1.44 (((~hskp4) | (~c2_1(a2191))) <=> ((~hskp4) | (~c2_1(a2191)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1690,plain,
% 1.20/1.44 (((~c2_1(a2191)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a2191)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1691,axiom,((~c2_1(a2191)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause232')).
% 1.20/1.44 tff(1692,plain,
% 1.20/1.44 ((~hskp4) | (~c2_1(a2191))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 1.20/1.44 tff(1693,plain,
% 1.20/1.44 ((~hskp4) | (~c2_1(a2191))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1692, 1689])).
% 1.20/1.44 tff(1694,plain,
% 1.20/1.44 (~c2_1(a2191)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1693, 1682])).
% 1.20/1.44 tff(1695,plain,
% 1.20/1.44 (((~hskp4) | c3_1(a2191)) <=> ((~hskp4) | c3_1(a2191))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1696,axiom,((~hskp4) | c3_1(a2191)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.20/1.44 tff(1697,plain,
% 1.20/1.44 ((~hskp4) | c3_1(a2191)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 1.20/1.44 tff(1698,plain,
% 1.20/1.44 ((~hskp4) | c3_1(a2191)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1697, 1695])).
% 1.20/1.44 tff(1699,plain,
% 1.20/1.44 ((~hskp4) | c3_1(a2191)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1698, 1695])).
% 1.20/1.44 tff(1700,plain,
% 1.20/1.44 ((~hskp4) | c3_1(a2191)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1699, 1695])).
% 1.20/1.44 tff(1701,plain,
% 1.20/1.44 ((~hskp4) | c3_1(a2191)),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1700, 1695])).
% 1.20/1.44 tff(1702,plain,
% 1.20/1.44 (c3_1(a2191)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1701, 1682])).
% 1.20/1.44 tff(1703,assumption,(~c1_1(a2222)), introduced(assumption)).
% 1.20/1.44 tff(1704,plain,
% 1.20/1.44 (hskp46 | hskp34),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[427, 150, 1586, 1585, 416, 1703])).
% 1.20/1.44 tff(1705,plain,
% 1.20/1.44 (hskp46),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1704, 328])).
% 1.20/1.44 tff(1706,plain,
% 1.20/1.44 (c2_1(a2218)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[436, 1705])).
% 1.20/1.44 tff(1707,plain,
% 1.20/1.44 (c0_1(a2218)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[444, 1705])).
% 1.20/1.44 tff(1708,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1709,plain,
% 1.20/1.44 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1710,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))))),
% 1.20/1.44 inference(monotonicity,[status(thm)],[1709])).
% 1.20/1.44 tff(1711,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)))),
% 1.20/1.44 inference(transitivity,[status(thm)],[1710, 1708])).
% 1.20/1.44 tff(1712,plain,
% 1.20/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2191) | c2_1(a2191) | (~c3_1(a2191)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 1.20/1.44 inference(quant_inst,[status(thm)],[])).
% 1.20/1.44 tff(1713,plain,
% 1.20/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c3_1(a2186) | c2_1(a2186) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 1.20/1.44 tff(1714,plain,
% 1.20/1.44 (~c1_1(a2218)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1713, 150, 1707, 1706, 482, 1702, 481, 480, 1694, 1688, 51])).
% 1.20/1.44 tff(1715,plain,
% 1.20/1.44 ($false),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[465, 150, 328, 72, 1707, 1706, 462, 1714])).
% 1.20/1.44 tff(1716,plain,(hskp34 | hskp33 | (~c0_1(a2186)) | c3_1(a2186) | c2_1(a2186) | (~c2_1(a2215)) | (~c1_1(a2215)) | c0_1(a2215) | (~c0_1(a2222)) | (~c3_1(a2222)) | c1_1(a2222) | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.20/1.44 tff(1717,plain,
% 1.20/1.44 (hskp34),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1716, 1659, 72, 1658, 1657, 1652, 1644, 1636, 1580, 1581, 1613, 1085])).
% 1.20/1.44 tff(1718,plain,
% 1.20/1.44 (c3_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[676, 1717])).
% 1.20/1.44 tff(1719,plain,
% 1.20/1.44 (c1_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[684, 1717])).
% 1.20/1.44 tff(1720,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1721,plain,
% 1.20/1.44 ((hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189))) <=> (hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1722,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))))),
% 1.20/1.44 inference(monotonicity,[status(thm)],[1721])).
% 1.20/1.44 tff(1723,plain,
% 1.20/1.44 (((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.20/1.44 inference(transitivity,[status(thm)],[1722, 1720])).
% 1.20/1.44 tff(1724,plain,
% 1.20/1.44 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | (hskp33 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | (~c3_1(a2189)) | (~c2_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.44 inference(quant_inst,[status(thm)],[])).
% 1.20/1.44 tff(1725,plain,
% 1.20/1.44 ((~![V: $i, U: $i] : (hskp33 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c1_1(V)))) | hskp33 | c0_1(a2215) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1724, 1723])).
% 1.20/1.44 tff(1726,plain,
% 1.20/1.44 (~c2_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1725, 150, 72, 1652, 1644, 1719, 1718, 1636, 71])).
% 1.20/1.44 tff(1727,plain,
% 1.20/1.44 (~c0_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[697, 1717])).
% 1.20/1.44 tff(1728,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1729,plain,
% 1.20/1.44 (((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189))) <=> (c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.44 inference(rewrite,[status(thm)],[])).
% 1.20/1.44 tff(1730,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 1.20/1.44 inference(monotonicity,[status(thm)],[1729])).
% 1.20/1.44 tff(1731,plain,
% 1.20/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.20/1.44 inference(transitivity,[status(thm)],[1730, 1728])).
% 1.20/1.44 tff(1732,plain,
% 1.20/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c2_1(a2181) | (~c0_1(a2181)) | (~c1_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)))),
% 1.20/1.44 inference(quant_inst,[status(thm)],[])).
% 1.20/1.44 tff(1733,plain,
% 1.20/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c1_1(a2181)) | c2_1(a2181) | (~ndr1_0) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 1.20/1.44 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 1.20/1.44 tff(1734,plain,
% 1.20/1.44 ($false),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1733, 150, 1719, 1718, 1727, 1525, 838, 97, 339, 1726])).
% 1.20/1.44 tff(1735,plain,(c2_1(a2181) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.44 tff(1736,plain,
% 1.20/1.44 (c2_1(a2181)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1735, 72])).
% 1.20/1.44 tff(1737,plain,
% 1.20/1.44 (~hskp0),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[875, 1736])).
% 1.20/1.44 tff(1738,plain,
% 1.20/1.44 (hskp34),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[767, 88, 1737, 72])).
% 1.20/1.44 tff(1739,plain,
% 1.20/1.44 (c3_1(a2235)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[627, 88])).
% 1.20/1.44 tff(1740,plain,
% 1.20/1.44 ($false),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[737, 1739, 747, 72, 1738, 96])).
% 1.20/1.44 tff(1741,plain,((~hskp53) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.44 tff(1742,plain,
% 1.20/1.44 (~hskp53),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1741, 72])).
% 1.20/1.44 tff(1743,plain,
% 1.20/1.44 (c1_1(a2186)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[491, 891, 1742, 87, 81])).
% 1.20/1.44 tff(1744,plain,
% 1.20/1.44 (hskp18),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[345, 150, 87, 891, 61, 1743])).
% 1.20/1.44 tff(1745,plain,
% 1.20/1.44 (c0_1(a2222)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[423, 1744])).
% 1.20/1.44 tff(1746,plain,
% 1.20/1.44 (~c2_1(a2222)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[352, 1744])).
% 1.20/1.44 tff(1747,plain,
% 1.20/1.44 (c3_1(a2222)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[390, 1744])).
% 1.20/1.44 tff(1748,plain,
% 1.20/1.44 (~c1_1(a2222)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1612, 1747, 1746, 1745])).
% 1.20/1.44 tff(1749,plain,
% 1.20/1.44 (hskp44),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1629, 150, 1745, 1747, 1746, 1623, 1748])).
% 1.20/1.44 tff(1750,plain,
% 1.20/1.44 (~c0_1(a2215)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1635, 1749])).
% 1.20/1.44 tff(1751,plain,
% 1.20/1.44 (c1_1(a2215)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1643, 1749])).
% 1.20/1.44 tff(1752,plain,
% 1.20/1.44 (c2_1(a2215)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1651, 1749])).
% 1.20/1.44 tff(1753,plain,
% 1.20/1.44 (hskp34),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1716, 1752, 1737, 81, 87, 891, 1751, 1750, 1745, 1747, 1748, 72])).
% 1.20/1.44 tff(1754,plain,
% 1.20/1.44 (c3_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[676, 1753])).
% 1.20/1.44 tff(1755,plain,
% 1.20/1.44 (c1_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[684, 1753])).
% 1.20/1.44 tff(1756,plain,
% 1.20/1.44 (~c2_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1725, 150, 72, 1752, 1751, 1755, 1754, 1750, 71])).
% 1.20/1.44 tff(1757,plain,
% 1.20/1.44 (~c0_1(a2189)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[697, 1753])).
% 1.20/1.44 tff(1758,plain,
% 1.20/1.44 ($false),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[725, 150, 1755, 1754, 81, 1757, 891, 339, 1743, 1756])).
% 1.20/1.44 tff(1759,plain,((~hskp32) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.20/1.44 tff(1760,plain,
% 1.20/1.44 (~hskp32),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1759, 72])).
% 1.20/1.44 tff(1761,plain,
% 1.20/1.44 (~hskp26),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1200, 328, 1737, 72])).
% 1.20/1.44 tff(1762,assumption,(~c3_1(a2181)), introduced(assumption)).
% 1.20/1.44 tff(1763,plain,
% 1.20/1.44 (hskp32 | hskp2 | c1_1(a2181) | c3_1(a2181)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[213, 150, 99, 207])).
% 1.20/1.44 tff(1764,plain,
% 1.20/1.44 (hskp2),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[1763, 1762, 100, 98])).
% 1.20/1.44 tff(1765,plain,
% 1.20/1.44 (~c2_1(a2187)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[220, 1764])).
% 1.20/1.44 tff(1766,plain,
% 1.20/1.44 (c1_1(a2187)),
% 1.20/1.44 inference(unit_resolution,[status(thm)],[276, 1764])).
% 1.20/1.45 tff(1767,plain,
% 1.20/1.45 (c3_1(a2187)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[228, 1764])).
% 1.20/1.45 tff(1768,plain,
% 1.20/1.45 (~hskp18),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1655, 100])).
% 1.20/1.45 tff(1769,assumption,(hskp10), introduced(assumption)).
% 1.20/1.45 tff(1770,plain,
% 1.20/1.45 (~c3_1(a2206)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1550, 1769])).
% 1.20/1.45 tff(1771,plain,
% 1.20/1.45 (~c2_1(a2206)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1556, 1769])).
% 1.20/1.45 tff(1772,plain,
% 1.20/1.45 (~c1_1(a2206)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1563, 150, 1381, 1771, 1770, 61])).
% 1.20/1.45 tff(1773,assumption,(~c2_1(a2187)), introduced(assumption)).
% 1.20/1.45 tff(1774,plain,
% 1.20/1.45 (~c0_1(a2206)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1569, 1769])).
% 1.20/1.45 tff(1775,assumption,(c3_1(a2187)), introduced(assumption)).
% 1.20/1.45 tff(1776,plain,
% 1.20/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1777,plain,
% 1.20/1.45 (((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206)) <=> (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1778,plain,
% 1.20/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | (c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206)))),
% 1.20/1.45 inference(monotonicity,[status(thm)],[1777])).
% 1.20/1.45 tff(1779,plain,
% 1.20/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206))),
% 1.20/1.45 inference(transitivity,[status(thm)],[1778, 1776])).
% 1.20/1.45 tff(1780,plain,
% 1.20/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c0_1(a2206) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206) | c3_1(a2206) | c1_1(a2206))),
% 1.20/1.45 inference(quant_inst,[status(thm)],[])).
% 1.20/1.45 tff(1781,plain,
% 1.20/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c3_1(W) | c1_1(W))) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | (~c0_1(a2187)) | c1_1(a2206)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.20/1.45 tff(1782,plain,
% 1.20/1.45 ((~c0_1(a2187)) | c1_1(a2206)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1781, 150, 1775, 1771, 1774, 1770, 1773, 197])).
% 1.20/1.45 tff(1783,plain,
% 1.20/1.45 (~c0_1(a2187)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1782, 1772])).
% 1.20/1.45 tff(1784,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1785,plain,
% 1.20/1.45 ((hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206)) <=> (hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1786,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206)))),
% 1.20/1.45 inference(monotonicity,[status(thm)],[1785])).
% 1.20/1.45 tff(1787,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206))),
% 1.20/1.45 inference(transitivity,[status(thm)],[1786, 1784])).
% 1.20/1.45 tff(1788,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2206) | c3_1(a2206) | c2_1(a2206))),
% 1.20/1.45 inference(quant_inst,[status(thm)],[])).
% 1.20/1.45 tff(1789,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c2_1(a2206) | c3_1(a2206) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c1_1(a2206)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.20/1.45 tff(1790,plain,
% 1.20/1.45 ($false),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1789, 150, 1010, 1775, 1771, 1770, 1773, 256, 1783, 1772])).
% 1.20/1.45 tff(1791,plain,((~hskp10) | hskp47 | (~c3_1(a2187)) | c2_1(a2187) | hskp18), inference(lemma,lemma(discharge,[]))).
% 1.20/1.45 tff(1792,plain,
% 1.20/1.45 (~hskp10),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1791, 1767, 1010, 1765, 1768])).
% 1.20/1.45 tff(1793,assumption,(~hskp10), introduced(assumption)).
% 1.20/1.45 tff(1794,assumption,(c1_1(a2187)), introduced(assumption)).
% 1.20/1.45 tff(1795,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1796,plain,
% 1.20/1.45 ((hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187))) <=> (hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1797,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187))))),
% 1.20/1.45 inference(monotonicity,[status(thm)],[1796])).
% 1.20/1.45 tff(1798,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187)))),
% 1.20/1.45 inference(transitivity,[status(thm)],[1797, 1795])).
% 1.20/1.45 tff(1799,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2187) | (~c3_1(a2187)) | (~c0_1(a2187)) | c2_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))),
% 1.20/1.45 inference(quant_inst,[status(thm)],[])).
% 1.20/1.45 tff(1800,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2187) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | (~c0_1(a2187))),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 1.20/1.45 tff(1801,plain,
% 1.20/1.45 (hskp10 | (~c0_1(a2187))),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1800, 150, 1775, 1794, 1773, 1537])).
% 1.20/1.45 tff(1802,plain,
% 1.20/1.45 (~c0_1(a2187)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1801, 1793])).
% 1.20/1.45 tff(1803,plain,
% 1.20/1.45 (^[U: $i] : refl((hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.20/1.45 inference(bind,[status(th)],[])).
% 1.20/1.45 tff(1804,plain,
% 1.20/1.45 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.20/1.45 inference(quant_intro,[status(thm)],[1803])).
% 1.20/1.45 tff(1805,plain,
% 1.20/1.45 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1806,plain,
% 1.20/1.45 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp41))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp41) <=> (hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) <=> (hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10) <=> ((hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp10))), rewrite(((hskp41 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp10) <=> (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10) <=> (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.20/1.45 inference(bind,[status(th)],[])).
% 1.20/1.45 tff(1807,plain,
% 1.20/1.45 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10) <=> ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.20/1.45 inference(quant_intro,[status(thm)],[1806])).
% 1.20/1.45 tff(1808,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp41) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause249')).
% 1.20/1.45 tff(1809,plain,
% 1.20/1.45 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 1.20/1.45 tff(1810,plain,
% 1.20/1.45 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1809, 1805])).
% 1.20/1.45 tff(1811,plain,(
% 1.20/1.45 ![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.20/1.45 inference(skolemize,[status(sab)],[1810])).
% 1.20/1.45 tff(1812,plain,
% 1.20/1.45 (![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1811, 1804])).
% 1.20/1.45 tff(1813,assumption,(c2_1(a2181)), introduced(assumption)).
% 1.20/1.45 tff(1814,plain,
% 1.20/1.45 (((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1815,plain,
% 1.20/1.45 ((hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181))) <=> (hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1816,plain,
% 1.20/1.45 (((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)))),
% 1.20/1.45 inference(monotonicity,[status(thm)],[1815])).
% 1.20/1.45 tff(1817,plain,
% 1.20/1.45 (((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.20/1.45 inference(transitivity,[status(thm)],[1816, 1814])).
% 1.20/1.45 tff(1818,plain,
% 1.20/1.45 ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp41 | hskp10 | (~ndr1_0) | c3_1(a2181) | c0_1(a2181) | (~c2_1(a2181)))),
% 1.20/1.45 inference(quant_inst,[status(thm)],[])).
% 1.20/1.45 tff(1819,plain,
% 1.20/1.45 ((~![U: $i] : (hskp41 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp41 | hskp10 | c0_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.20/1.45 tff(1820,plain,
% 1.20/1.45 (hskp41 | hskp10 | c0_1(a2181) | c3_1(a2181)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1819, 150, 1813, 1812])).
% 1.20/1.45 tff(1821,plain,
% 1.20/1.45 (hskp41),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1820, 1793, 99, 1762])).
% 1.20/1.45 tff(1822,plain,
% 1.20/1.45 (((~hskp41) | (~c0_1(a2205))) <=> ((~hskp41) | (~c0_1(a2205)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1823,plain,
% 1.20/1.45 (((~c0_1(a2205)) | (~hskp41)) <=> ((~hskp41) | (~c0_1(a2205)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1824,axiom,((~c0_1(a2205)) | (~hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.20/1.45 tff(1825,plain,
% 1.20/1.45 ((~hskp41) | (~c0_1(a2205))),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.20/1.45 tff(1826,plain,
% 1.20/1.45 ((~hskp41) | (~c0_1(a2205))),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1825, 1822])).
% 1.20/1.45 tff(1827,plain,
% 1.20/1.45 (~c0_1(a2205)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1826, 1821])).
% 1.20/1.45 tff(1828,plain,
% 1.20/1.45 (((~hskp41) | c1_1(a2205)) <=> ((~hskp41) | c1_1(a2205))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1829,axiom,((~hskp41) | c1_1(a2205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.20/1.45 tff(1830,plain,
% 1.20/1.45 ((~hskp41) | c1_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.20/1.45 tff(1831,plain,
% 1.20/1.45 ((~hskp41) | c1_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1830, 1828])).
% 1.20/1.45 tff(1832,plain,
% 1.20/1.45 ((~hskp41) | c1_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1831, 1828])).
% 1.20/1.45 tff(1833,plain,
% 1.20/1.45 ((~hskp41) | c1_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1832, 1828])).
% 1.20/1.45 tff(1834,plain,
% 1.20/1.45 ((~hskp41) | c1_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1833, 1828])).
% 1.20/1.45 tff(1835,plain,
% 1.20/1.45 (c1_1(a2205)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1834, 1821])).
% 1.20/1.45 tff(1836,plain,
% 1.20/1.45 (((~hskp41) | c2_1(a2205)) <=> ((~hskp41) | c2_1(a2205))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1837,axiom,((~hskp41) | c2_1(a2205)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.20/1.45 tff(1838,plain,
% 1.20/1.45 ((~hskp41) | c2_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 1.20/1.45 tff(1839,plain,
% 1.20/1.45 ((~hskp41) | c2_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1838, 1836])).
% 1.20/1.45 tff(1840,plain,
% 1.20/1.45 ((~hskp41) | c2_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1839, 1836])).
% 1.20/1.45 tff(1841,plain,
% 1.20/1.45 ((~hskp41) | c2_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1840, 1836])).
% 1.20/1.45 tff(1842,plain,
% 1.20/1.45 ((~hskp41) | c2_1(a2205)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1841, 1836])).
% 1.20/1.45 tff(1843,plain,
% 1.20/1.45 (c2_1(a2205)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1842, 1821])).
% 1.20/1.45 tff(1844,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1845,plain,
% 1.20/1.45 ((hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187))) <=> (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1846,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205))))),
% 1.20/1.45 inference(monotonicity,[status(thm)],[1845])).
% 1.20/1.45 tff(1847,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205)))),
% 1.20/1.45 inference(transitivity,[status(thm)],[1846, 1844])).
% 1.20/1.45 tff(1848,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2187) | (~c3_1(a2187)) | (~c1_1(a2187)))),
% 1.20/1.45 inference(quant_inst,[status(thm)],[])).
% 1.20/1.45 tff(1849,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2205)) | (~c1_1(a2205))),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.20/1.45 tff(1850,plain,
% 1.20/1.45 ($false),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1849, 150, 1167, 1843, 1835, 1775, 1794, 1827, 41, 1802])).
% 1.20/1.45 tff(1851,plain,(hskp10 | hskp48 | (~c3_1(a2187)) | (~c1_1(a2187)) | c2_1(a2187) | c0_1(a2181) | c3_1(a2181) | (~c2_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.45 tff(1852,plain,
% 1.20/1.45 (hskp48),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1851, 1792, 1767, 1766, 1765, 99, 1762, 1736])).
% 1.20/1.45 tff(1853,plain,
% 1.20/1.45 (~c0_1(a2228)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1110, 1852])).
% 1.20/1.45 tff(1854,plain,
% 1.20/1.45 (c2_1(a2228)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1118, 1852])).
% 1.20/1.45 tff(1855,plain,
% 1.20/1.45 (c3_1(a2228)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1126, 1852])).
% 1.20/1.45 tff(1856,plain,
% 1.20/1.45 (~c1_1(a2228)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1133, 150, 72, 1855, 1854, 1853, 71])).
% 1.20/1.45 tff(1857,plain,
% 1.20/1.45 (hskp10 | (~c0_1(a2187))),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1800, 150, 1767, 1766, 1765, 1537])).
% 1.20/1.45 tff(1858,plain,
% 1.20/1.45 (~c0_1(a2187)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1857, 1792])).
% 1.20/1.45 tff(1859,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1860,plain,
% 1.20/1.45 ((hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1861,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228)))),
% 1.20/1.45 inference(monotonicity,[status(thm)],[1860])).
% 1.20/1.45 tff(1862,plain,
% 1.20/1.45 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.20/1.45 inference(transitivity,[status(thm)],[1861, 1859])).
% 1.20/1.45 tff(1863,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2187) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 1.20/1.45 inference(quant_inst,[status(thm)],[])).
% 1.20/1.45 tff(1864,plain,
% 1.20/1.45 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2187)) | (~c3_1(a2187)) | c0_1(a2187) | (~c2_1(a2228)) | c1_1(a2228)),
% 1.20/1.45 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 1.20/1.45 tff(1865,plain,
% 1.20/1.45 ($false),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1864, 150, 1285, 1854, 1767, 1766, 1853, 1144, 1858, 1856])).
% 1.20/1.45 tff(1866,plain,(c3_1(a2181) | hskp26 | hskp33 | c0_1(a2181) | hskp47 | hskp32 | c1_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.20/1.45 tff(1867,plain,
% 1.20/1.45 (c3_1(a2181)),
% 1.20/1.45 inference(unit_resolution,[status(thm)],[1866, 1761, 72, 99, 1186, 100, 98])).
% 1.20/1.45 tff(1868,plain,
% 1.20/1.45 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.20/1.45 inference(bind,[status(th)],[])).
% 1.20/1.45 tff(1869,plain,
% 1.20/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.20/1.45 inference(quant_intro,[status(thm)],[1868])).
% 1.20/1.45 tff(1870,plain,
% 1.20/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.20/1.45 inference(rewrite,[status(thm)],[])).
% 1.20/1.45 tff(1871,plain,
% 1.20/1.45 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.29/1.45 inference(bind,[status(th)],[])).
% 1.29/1.45 tff(1872,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.29/1.45 inference(quant_intro,[status(thm)],[1871])).
% 1.29/1.45 tff(1873,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause289')).
% 1.29/1.45 tff(1874,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 1.29/1.45 tff(1875,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[1874, 1870])).
% 1.29/1.45 tff(1876,plain,(
% 1.29/1.45 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.29/1.45 inference(skolemize,[status(sab)],[1875])).
% 1.29/1.45 tff(1877,plain,
% 1.29/1.45 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.29/1.45 inference(modus_ponens,[status(thm)],[1876, 1869])).
% 1.29/1.45 tff(1878,plain,
% 1.29/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(1879,plain,
% 1.29/1.45 (((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196))) <=> (c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))),
% 1.29/1.45 inference(rewrite,[status(thm)],[])).
% 1.29/1.45 tff(1880,plain,
% 1.29/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196))))),
% 1.29/1.45 inference(monotonicity,[status(thm)],[1879])).
% 1.29/1.45 tff(1881,plain,
% 1.29/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196)))),
% 1.29/1.45 inference(transitivity,[status(thm)],[1880, 1878])).
% 1.29/1.45 tff(1882,plain,
% 1.29/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | c0_1(a2196) | c3_1(a2196) | (~c2_1(a2196)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1883,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c3_1(a2196) | (~c2_1(a2196))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1882, 1881])).
% 1.29/1.46 tff(1884,plain,
% 1.29/1.46 (c3_1(a2196)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1883, 150, 643, 635, 99, 98, 1813, 1877, 101])).
% 1.29/1.46 tff(1885,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1886,plain,
% 1.29/1.46 ((hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181))) <=> (hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1887,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1886])).
% 1.29/1.46 tff(1888,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1887, 1885])).
% 1.29/1.46 tff(1889,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2196) | (~c1_1(a2196)) | (~c3_1(a2196)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1890,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2196) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2196)) | (~c3_1(a2196))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 1.29/1.46 tff(1891,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1890, 150, 1285, 651, 635, 99, 98, 1813, 1144, 1884])).
% 1.29/1.46 tff(1892,plain,((~hskp37) | hskp26 | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~c3_1(a2181))), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1893,plain,
% 1.29/1.46 (~hskp37),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1892, 1761, 99, 98, 1736, 1867])).
% 1.29/1.46 tff(1894,plain,
% 1.29/1.46 (hskp6),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[567, 1893, 328])).
% 1.29/1.46 tff(1895,plain,
% 1.29/1.46 (~c1_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[573, 1894])).
% 1.29/1.46 tff(1896,plain,
% 1.29/1.46 (~c3_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[996, 1894])).
% 1.29/1.46 tff(1897,plain,
% 1.29/1.46 (~c0_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[579, 1894])).
% 1.29/1.46 tff(1898,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1899,plain,
% 1.29/1.46 (((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197))) <=> (c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1900,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1899])).
% 1.29/1.46 tff(1901,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1900, 1898])).
% 1.29/1.46 tff(1902,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2181) | (~c3_1(a2181)) | (~c2_1(a2181)) | c0_1(a2197) | c1_1(a2197) | (~c2_1(a2197)) | c0_1(a2197) | c3_1(a2197) | (~c2_1(a2197)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1903,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | (~c2_1(a2197))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.29/1.46 tff(1904,plain,
% 1.29/1.46 (~c2_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1903, 150, 1897, 1896, 1895, 98, 1736, 1877, 1867])).
% 1.29/1.46 tff(1905,assumption,(hskp6), introduced(assumption)).
% 1.29/1.46 tff(1906,plain,
% 1.29/1.46 (~c1_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[573, 1905])).
% 1.29/1.46 tff(1907,plain,
% 1.29/1.46 (~c3_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[996, 1905])).
% 1.29/1.46 tff(1908,plain,
% 1.29/1.46 (~c0_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[579, 1905])).
% 1.29/1.46 tff(1909,plain,
% 1.29/1.46 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1910,plain,
% 1.29/1.46 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197)) <=> (hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1911,plain,
% 1.29/1.46 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0)))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1910])).
% 1.29/1.46 tff(1912,plain,
% 1.29/1.46 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1911, 1909])).
% 1.29/1.46 tff(1913,plain,
% 1.29/1.46 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2197) | c3_1(a2197) | c0_1(a2197))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1914,plain,
% 1.29/1.46 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2197) | c3_1(a2197) | c1_1(a2197) | (~ndr1_0)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 1.29/1.46 tff(1915,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1914, 150, 100, 1334, 1908, 1907, 1906, 207])).
% 1.29/1.46 tff(1916,plain,((~hskp6) | hskp32 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1917,plain,
% 1.29/1.46 (hskp2),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1916, 1894, 100])).
% 1.29/1.46 tff(1918,plain,
% 1.29/1.46 (~c2_1(a2187)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[220, 1917])).
% 1.29/1.46 tff(1919,plain,
% 1.29/1.46 (c1_1(a2187)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[276, 1917])).
% 1.29/1.46 tff(1920,plain,
% 1.29/1.46 (c3_1(a2187)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[228, 1917])).
% 1.29/1.46 tff(1921,plain,
% 1.29/1.46 (~hskp10),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1791, 1920, 1186, 1918, 1768])).
% 1.29/1.46 tff(1922,plain,
% 1.29/1.46 (~c0_1(a2187)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1800, 150, 1921, 1920, 1919, 1918, 1537])).
% 1.29/1.46 tff(1923,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1924,plain,
% 1.29/1.46 ((hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197)) <=> (hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1925,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197)))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1924])).
% 1.29/1.46 tff(1926,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))) <=> ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1925, 1923])).
% 1.29/1.46 tff(1927,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (hskp47 | (~ndr1_0) | c2_1(a2187) | c0_1(a2187) | (~c3_1(a2187)) | c1_1(a2197) | c3_1(a2197) | c2_1(a2197))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1928,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp47 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | hskp47 | c3_1(a2197) | c1_1(a2197) | c2_1(a2187) | (~ndr1_0) | (~c3_1(a2187)) | c0_1(a2187) | c2_1(a2197)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 1.29/1.46 tff(1929,plain,
% 1.29/1.46 (c0_1(a2187) | c2_1(a2197)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1928, 150, 1186, 1920, 1896, 1895, 1918, 256])).
% 1.29/1.46 tff(1930,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1929, 1922, 1904])).
% 1.29/1.46 tff(1931,plain,(hskp34 | c1_1(a2181) | hskp32 | c0_1(a2181) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1932,plain,
% 1.29/1.46 (hskp34),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1931, 98, 100, 99, 72])).
% 1.29/1.46 tff(1933,plain,
% 1.29/1.46 (~c0_1(a2189)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[697, 1932])).
% 1.29/1.46 tff(1934,plain,
% 1.29/1.46 (c3_1(a2189)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[676, 1932])).
% 1.29/1.46 tff(1935,plain,
% 1.29/1.46 (c1_1(a2189)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[684, 1932])).
% 1.29/1.46 tff(1936,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1937,plain,
% 1.29/1.46 ((hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181))) <=> (hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1938,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1937])).
% 1.29/1.46 tff(1939,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1938, 1936])).
% 1.29/1.46 tff(1940,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2189) | (~c1_1(a2189)) | (~c3_1(a2189)) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1941,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2189) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 1.29/1.46 tff(1942,plain,
% 1.29/1.46 (hskp26),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1941, 150, 1935, 1934, 1933, 99, 98, 1736, 1144])).
% 1.29/1.46 tff(1943,plain,
% 1.29/1.46 (c2_1(a2178)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1075, 1942])).
% 1.29/1.46 tff(1944,plain,
% 1.29/1.46 (c0_1(a2178)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1083, 1942])).
% 1.29/1.46 tff(1945,plain,
% 1.29/1.46 (~c1_1(a2178)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1088, 150, 1737, 1944, 1943, 758])).
% 1.29/1.46 tff(1946,plain,
% 1.29/1.46 (~c3_1(a2178)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1094, 1942])).
% 1.29/1.46 tff(1947,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1948,plain,
% 1.29/1.46 (((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178))) <=> (c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1949,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1948])).
% 1.29/1.46 tff(1950,plain,
% 1.29/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1949, 1947])).
% 1.29/1.46 tff(1951,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2181) | c0_1(a2181) | (~c2_1(a2181)) | c3_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178)) | c3_1(a2178) | c1_1(a2178) | (~c0_1(a2178)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1952,plain,
% 1.29/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a2178) | c0_1(a2181) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0) | c1_1(a2178) | (~c0_1(a2178)) | (~c2_1(a2178))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 1.29/1.46 tff(1953,plain,
% 1.29/1.46 ($false),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1952, 150, 1944, 1943, 1946, 99, 98, 1736, 974, 1945])).
% 1.29/1.46 tff(1954,plain,(c1_1(a2181) | c0_1(a2181) | hskp32 | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.29/1.46 tff(1955,plain,
% 1.29/1.46 (c1_1(a2181)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1954, 100, 99, 72])).
% 1.29/1.46 tff(1956,plain,
% 1.29/1.46 (^[U: $i] : refl((hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(1957,plain,
% 1.29/1.46 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[1956])).
% 1.29/1.46 tff(1958,plain,
% 1.29/1.46 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1959,plain,
% 1.29/1.46 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp31))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp31) <=> (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31) <=> (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 1.29/1.46 inference(bind,[status(th)],[])).
% 1.29/1.46 tff(1960,plain,
% 1.29/1.46 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31) <=> ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.29/1.46 inference(quant_intro,[status(thm)],[1959])).
% 1.29/1.46 tff(1961,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp18) | hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause260')).
% 1.29/1.46 tff(1962,plain,
% 1.29/1.46 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1961, 1960])).
% 1.29/1.46 tff(1963,plain,
% 1.29/1.46 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1962, 1958])).
% 1.29/1.46 tff(1964,plain,(
% 1.29/1.46 ![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.29/1.46 inference(skolemize,[status(sab)],[1963])).
% 1.29/1.46 tff(1965,plain,
% 1.29/1.46 (![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1964, 1957])).
% 1.29/1.46 tff(1966,plain,
% 1.29/1.46 (((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1967,plain,
% 1.29/1.46 ((hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181))) <=> (hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1968,plain,
% 1.29/1.46 (((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[1967])).
% 1.29/1.46 tff(1969,plain,
% 1.29/1.46 (((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.29/1.46 inference(transitivity,[status(thm)],[1968, 1966])).
% 1.29/1.46 tff(1970,plain,
% 1.29/1.46 ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp31 | hskp18 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(1971,plain,
% 1.29/1.46 ((~![U: $i] : (hskp31 | hskp18 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp31 | hskp18 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 1.29/1.46 tff(1972,plain,
% 1.29/1.46 (hskp31 | hskp18 | (~c1_1(a2181)) | c3_1(a2181)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1971, 150, 1736, 1965])).
% 1.29/1.46 tff(1973,plain,
% 1.29/1.46 (hskp31),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1972, 1762, 1768, 1955])).
% 1.29/1.46 tff(1974,plain,
% 1.29/1.46 (((~hskp31) | (~c2_1(a2185))) <=> ((~hskp31) | (~c2_1(a2185)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1975,plain,
% 1.29/1.46 (((~c2_1(a2185)) | (~hskp31)) <=> ((~hskp31) | (~c2_1(a2185)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1976,axiom,((~c2_1(a2185)) | (~hskp31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.29/1.46 tff(1977,plain,
% 1.29/1.46 ((~hskp31) | (~c2_1(a2185))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1976, 1975])).
% 1.29/1.46 tff(1978,plain,
% 1.29/1.46 ((~hskp31) | (~c2_1(a2185))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1977, 1974])).
% 1.29/1.46 tff(1979,plain,
% 1.29/1.46 (~c2_1(a2185)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1978, 1973])).
% 1.29/1.46 tff(1980,plain,
% 1.29/1.46 (((~hskp31) | c3_1(a2185)) <=> ((~hskp31) | c3_1(a2185))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1981,axiom,((~hskp31) | c3_1(a2185)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.29/1.46 tff(1982,plain,
% 1.29/1.46 ((~hskp31) | c3_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 1.29/1.46 tff(1983,plain,
% 1.29/1.46 ((~hskp31) | c3_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1982, 1980])).
% 1.29/1.46 tff(1984,plain,
% 1.29/1.46 ((~hskp31) | c3_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1983, 1980])).
% 1.29/1.46 tff(1985,plain,
% 1.29/1.46 ((~hskp31) | c3_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1984, 1980])).
% 1.29/1.46 tff(1986,plain,
% 1.29/1.46 ((~hskp31) | c3_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1985, 1980])).
% 1.29/1.46 tff(1987,plain,
% 1.29/1.46 (c3_1(a2185)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1986, 1973])).
% 1.29/1.46 tff(1988,plain,
% 1.29/1.46 (((~hskp31) | c1_1(a2185)) <=> ((~hskp31) | c1_1(a2185))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(1989,axiom,((~hskp31) | c1_1(a2185)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.29/1.46 tff(1990,plain,
% 1.29/1.46 ((~hskp31) | c1_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1989, 1988])).
% 1.29/1.46 tff(1991,plain,
% 1.29/1.46 ((~hskp31) | c1_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1990, 1988])).
% 1.29/1.46 tff(1992,plain,
% 1.29/1.46 ((~hskp31) | c1_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1991, 1988])).
% 1.29/1.46 tff(1993,plain,
% 1.29/1.46 ((~hskp31) | c1_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1992, 1988])).
% 1.29/1.46 tff(1994,plain,
% 1.29/1.46 ((~hskp31) | c1_1(a2185)),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[1993, 1988])).
% 1.29/1.46 tff(1995,plain,
% 1.29/1.46 (c1_1(a2185)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1994, 1973])).
% 1.29/1.46 tff(1996,assumption,(~c2_1(a2185)), introduced(assumption)).
% 1.29/1.46 tff(1997,assumption,(c3_1(a2185)), introduced(assumption)).
% 1.29/1.46 tff(1998,assumption,(c1_1(a2185)), introduced(assumption)).
% 1.29/1.46 tff(1999,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(2000,plain,
% 1.29/1.46 ((hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185))) <=> (hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(2001,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185))))),
% 1.29/1.46 inference(monotonicity,[status(thm)],[2000])).
% 1.29/1.46 tff(2002,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185)))),
% 1.29/1.46 inference(transitivity,[status(thm)],[2001, 1999])).
% 1.29/1.46 tff(2003,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2185) | (~c3_1(a2185)) | (~c0_1(a2185)) | c2_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))),
% 1.29/1.46 inference(quant_inst,[status(thm)],[])).
% 1.29/1.46 tff(2004,plain,
% 1.29/1.46 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp10 | c2_1(a2185) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | (~c0_1(a2185))),
% 1.29/1.46 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.29/1.46 tff(2005,plain,
% 1.29/1.46 (hskp10 | (~c0_1(a2185))),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[2004, 150, 1998, 1997, 1996, 1537])).
% 1.29/1.46 tff(2006,plain,
% 1.29/1.46 (~c0_1(a2185)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[2005, 1793])).
% 1.29/1.46 tff(2007,plain,
% 1.29/1.46 (hskp41 | hskp10 | c0_1(a2181) | c3_1(a2181)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1819, 150, 1736, 1812])).
% 1.29/1.46 tff(2008,plain,
% 1.29/1.46 (hskp41),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[2007, 1793, 99, 1762])).
% 1.29/1.46 tff(2009,plain,
% 1.29/1.46 (~c0_1(a2205)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1826, 2008])).
% 1.29/1.46 tff(2010,plain,
% 1.29/1.46 (c1_1(a2205)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1834, 2008])).
% 1.29/1.46 tff(2011,plain,
% 1.29/1.46 (c2_1(a2205)),
% 1.29/1.46 inference(unit_resolution,[status(thm)],[1842, 2008])).
% 1.29/1.46 tff(2012,plain,
% 1.29/1.46 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))),
% 1.29/1.46 inference(rewrite,[status(thm)],[])).
% 1.29/1.46 tff(2013,plain,
% 1.29/1.46 ((hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185))) <=> (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2014,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2013])).
% 1.29/1.47 tff(2015,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2014, 2012])).
% 1.29/1.47 tff(2016,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2205) | (~c1_1(a2205)) | (~c2_1(a2205)) | c0_1(a2185) | (~c3_1(a2185)) | (~c1_1(a2185)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2017,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2205) | (~ndr1_0) | (~c2_1(a2205)) | (~c1_1(a2205)) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 1.29/1.47 tff(2018,plain,
% 1.29/1.47 (hskp48),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2017, 150, 2011, 2010, 1998, 1997, 2009, 41, 2006])).
% 1.29/1.47 tff(2019,plain,
% 1.29/1.47 (~c0_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1110, 2018])).
% 1.29/1.47 tff(2020,plain,
% 1.29/1.47 (c2_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1118, 2018])).
% 1.29/1.47 tff(2021,plain,
% 1.29/1.47 (c3_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1126, 2018])).
% 1.29/1.47 tff(2022,plain,
% 1.29/1.47 (~c1_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1133, 150, 72, 2021, 2020, 2019, 71])).
% 1.29/1.47 tff(2023,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2024,plain,
% 1.29/1.47 ((hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2025,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2024])).
% 1.29/1.47 tff(2026,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2025, 2023])).
% 1.29/1.47 tff(2027,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | c0_1(a2185) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2028,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp26 | c0_1(a2228) | (~ndr1_0) | (~c1_1(a2185)) | (~c3_1(a2185)) | c0_1(a2185) | (~c2_1(a2228)) | c1_1(a2228)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 1.29/1.47 tff(2029,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2028, 150, 1285, 2020, 1998, 1997, 2019, 1144, 2006, 2022])).
% 1.29/1.47 tff(2030,plain,(hskp10 | hskp26 | (~c1_1(a2185)) | (~c3_1(a2185)) | hskp33 | c2_1(a2185) | c0_1(a2181) | c3_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(2031,plain,
% 1.29/1.47 (hskp10),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2030, 1761, 1995, 1987, 72, 1979, 99, 1762])).
% 1.29/1.47 tff(2032,plain,
% 1.29/1.47 (~c3_1(a2206)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1550, 2031])).
% 1.29/1.47 tff(2033,plain,
% 1.29/1.47 (~c2_1(a2206)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1556, 2031])).
% 1.29/1.47 tff(2034,assumption,(hskp4), introduced(assumption)).
% 1.29/1.47 tff(2035,plain,
% 1.29/1.47 (~c1_1(a2191)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1687, 2034])).
% 1.29/1.47 tff(2036,plain,
% 1.29/1.47 (~c2_1(a2191)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1693, 2034])).
% 1.29/1.47 tff(2037,plain,
% 1.29/1.47 (c3_1(a2191)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1701, 2034])).
% 1.29/1.47 tff(2038,plain,
% 1.29/1.47 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2039,plain,
% 1.29/1.47 ((hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191))) <=> (hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2040,plain,
% 1.29/1.47 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2039])).
% 1.29/1.47 tff(2041,plain,
% 1.29/1.47 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2040, 2038])).
% 1.29/1.47 tff(2042,plain,
% 1.29/1.47 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2043,plain,
% 1.29/1.47 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 1.29/1.47 tff(2044,plain,
% 1.29/1.47 (hskp58),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2043, 150, 2037, 2036, 2035, 121])).
% 1.29/1.47 tff(2045,plain,
% 1.29/1.47 (~c1_1(a2252)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[163, 2044])).
% 1.29/1.47 tff(2046,plain,
% 1.29/1.47 (~c2_1(a2252)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[169, 2044])).
% 1.29/1.47 tff(2047,plain,
% 1.29/1.47 (c0_1(a2252)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[177, 2044])).
% 1.29/1.47 tff(2048,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2049,plain,
% 1.29/1.47 ((hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2050,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2049])).
% 1.29/1.47 tff(2051,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2050, 2048])).
% 1.29/1.47 tff(2052,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp32 | (~ndr1_0) | c2_1(a2191) | c1_1(a2191) | (~c3_1(a2191)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2053,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp32 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp32 | c2_1(a2252) | c1_1(a2252) | c2_1(a2191) | c1_1(a2191) | (~ndr1_0) | (~c3_1(a2191)) | (~c0_1(a2252))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 1.29/1.47 tff(2054,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2053, 150, 100, 2047, 2037, 2046, 2045, 2036, 2035, 111])).
% 1.29/1.47 tff(2055,plain,((~hskp4) | hskp32), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(2056,plain,
% 1.29/1.47 (~hskp4),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2055, 100])).
% 1.29/1.47 tff(2057,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2058,plain,
% 1.29/1.47 ((hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181))) <=> (hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2059,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2058])).
% 1.29/1.47 tff(2060,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2059, 2057])).
% 1.29/1.47 tff(2061,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2206) | c3_1(a2206) | (~c1_1(a2206)) | c0_1(a2181) | (~c2_1(a2181)) | (~c1_1(a2181)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2062,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp4 | c2_1(a2206) | c3_1(a2206) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c1_1(a2206))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 1.29/1.47 tff(2063,plain,
% 1.29/1.47 (~c1_1(a2206)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2062, 150, 2056, 2033, 2032, 99, 1955, 1736, 1671])).
% 1.29/1.47 tff(2064,plain,
% 1.29/1.47 (~c0_1(a2206)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1569, 2031])).
% 1.29/1.47 tff(2065,plain,
% 1.29/1.47 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2066,plain,
% 1.29/1.47 ((hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206)) <=> (hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2067,plain,
% 1.29/1.47 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2066])).
% 1.29/1.47 tff(2068,plain,
% 1.29/1.47 (((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206))) <=> ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2067, 2065])).
% 1.29/1.47 tff(2069,plain,
% 1.29/1.47 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | (hskp32 | hskp2 | (~ndr1_0) | c1_1(a2206) | c3_1(a2206) | c0_1(a2206))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2070,plain,
% 1.29/1.47 ((~![U: $i] : (hskp32 | hskp2 | (~ndr1_0) | c1_1(U) | c3_1(U) | c0_1(U))) | hskp32 | hskp2 | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | c1_1(a2206)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 1.29/1.47 tff(2071,plain,
% 1.29/1.47 (hskp2),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2070, 150, 100, 2064, 2032, 207, 2063])).
% 1.29/1.47 tff(2072,plain,
% 1.29/1.47 (c3_1(a2187)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[228, 2071])).
% 1.29/1.47 tff(2073,plain,
% 1.29/1.47 (~c2_1(a2187)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[220, 2071])).
% 1.29/1.47 tff(2074,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1791, 2073, 2072, 1186, 2031, 1768])).
% 1.29/1.47 tff(2075,plain,(hskp34 | hskp32 | c0_1(a2181) | hskp33 | c3_1(a2181)), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(2076,plain,
% 1.29/1.47 (hskp34),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2075, 1762, 99, 72, 100])).
% 1.29/1.47 tff(2077,plain,
% 1.29/1.47 (~c0_1(a2189)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[697, 2076])).
% 1.29/1.47 tff(2078,plain,
% 1.29/1.47 (c3_1(a2189)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[676, 2076])).
% 1.29/1.47 tff(2079,plain,
% 1.29/1.47 (c1_1(a2189)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[684, 2076])).
% 1.29/1.47 tff(2080,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2081,plain,
% 1.29/1.47 ((hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2082,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2081])).
% 1.29/1.47 tff(2083,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2082, 2080])).
% 1.29/1.47 tff(2084,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2085,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2189) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 1.29/1.47 tff(2086,plain,
% 1.29/1.47 (hskp48),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2085, 150, 2079, 2078, 2077, 99, 1955, 1736, 41])).
% 1.29/1.47 tff(2087,plain,
% 1.29/1.47 (~c0_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1110, 2086])).
% 1.29/1.47 tff(2088,plain,
% 1.29/1.47 (c2_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1118, 2086])).
% 1.29/1.47 tff(2089,plain,
% 1.29/1.47 (c3_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1126, 2086])).
% 1.29/1.47 tff(2090,plain,
% 1.29/1.47 (~c1_1(a2228)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1133, 150, 72, 2089, 2088, 2087, 71])).
% 1.29/1.47 tff(2091,plain,
% 1.29/1.47 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2092,plain,
% 1.29/1.47 ((hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181))) <=> (hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2093,plain,
% 1.29/1.47 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2092])).
% 1.29/1.47 tff(2094,plain,
% 1.29/1.47 (((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2093, 2091])).
% 1.29/1.47 tff(2095,plain,
% 1.29/1.47 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp17 | (~ndr1_0) | c3_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2096,plain,
% 1.29/1.47 ((~![U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp17 | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | c3_1(a2181)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 1.29/1.47 tff(2097,plain,
% 1.29/1.47 (hskp17 | (~c1_1(a2181)) | c3_1(a2181)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2096, 150, 1736, 1345])).
% 1.29/1.47 tff(2098,plain,
% 1.29/1.47 (hskp17),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2097, 1762, 1955])).
% 1.29/1.47 tff(2099,plain,
% 1.29/1.47 (~c3_1(a2221)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1418, 2098])).
% 1.29/1.47 tff(2100,plain,
% 1.29/1.47 (~c0_1(a2221)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1424, 2098])).
% 1.29/1.47 tff(2101,plain,
% 1.29/1.47 (c2_1(a2221)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1439, 2098])).
% 1.29/1.47 tff(2102,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2103,plain,
% 1.29/1.47 (((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221))) <=> (c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2104,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2103])).
% 1.29/1.47 tff(2105,plain,
% 1.29/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2104, 2102])).
% 1.29/1.47 tff(2106,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)) | c0_1(a2221) | c3_1(a2221) | (~c2_1(a2221)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2107,plain,
% 1.29/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2221) | c3_1(a2221) | (~ndr1_0) | (~c2_1(a2221)) | (~c2_1(a2228)) | c1_1(a2228) | (~c3_1(a2228))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.29/1.47 tff(2108,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2107, 150, 2089, 2088, 2101, 2087, 2100, 2099, 1877, 2090])).
% 1.29/1.47 tff(2109,plain,(c3_1(a2181) | hskp33 | c0_1(a2181) | hskp32), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(2110,plain,
% 1.29/1.47 (c3_1(a2181)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2109, 100, 99, 72])).
% 1.29/1.47 tff(2111,plain,
% 1.29/1.47 (~hskp48),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[1165, 2110, 99, 1955, 72])).
% 1.29/1.47 tff(2112,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2113,plain,
% 1.29/1.47 ((hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181))) <=> (hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2114,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181))))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2113])).
% 1.29/1.47 tff(2115,plain,
% 1.29/1.47 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2114, 2112])).
% 1.29/1.47 tff(2116,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | c0_1(a2181) | (~c3_1(a2181)) | (~c1_1(a2181)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2117,plain,
% 1.29/1.47 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2181) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181))),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 1.29/1.47 tff(2118,plain,
% 1.29/1.47 (hskp48 | (~c1_1(a2181)) | (~c3_1(a2181))),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2117, 150, 99, 1736, 41])).
% 1.29/1.47 tff(2119,plain,
% 1.29/1.47 ($false),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2118, 2111, 2110, 1955])).
% 1.29/1.47 tff(2120,plain,(hskp32 | c0_1(a2181) | hskp33), inference(lemma,lemma(discharge,[]))).
% 1.29/1.47 tff(2121,plain,
% 1.29/1.47 (c0_1(a2181)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2120, 1760, 72])).
% 1.29/1.47 tff(2122,plain,
% 1.29/1.47 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2123,plain,
% 1.29/1.47 ((hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181))) <=> (hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2124,plain,
% 1.29/1.47 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2123])).
% 1.29/1.47 tff(2125,plain,
% 1.29/1.47 (((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0))),
% 1.29/1.47 inference(transitivity,[status(thm)],[2124, 2122])).
% 1.29/1.47 tff(2126,plain,
% 1.29/1.47 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp0 | (~ndr1_0) | (~c1_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)))),
% 1.29/1.47 inference(quant_inst,[status(thm)],[])).
% 1.29/1.47 tff(2127,plain,
% 1.29/1.47 ((~![U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp0 | (~c0_1(a2181)) | (~c1_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0)),
% 1.29/1.47 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 1.29/1.47 tff(2128,plain,
% 1.29/1.47 ((~c0_1(a2181)) | (~c1_1(a2181))),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2127, 150, 1737, 1736, 758])).
% 1.29/1.47 tff(2129,plain,
% 1.29/1.47 (~c1_1(a2181)),
% 1.29/1.47 inference(unit_resolution,[status(thm)],[2128, 2121])).
% 1.29/1.47 tff(2130,plain,
% 1.29/1.47 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2131,plain,
% 1.29/1.47 ((hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181))) <=> (hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))),
% 1.29/1.47 inference(rewrite,[status(thm)],[])).
% 1.29/1.47 tff(2132,plain,
% 1.29/1.47 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0)))),
% 1.29/1.47 inference(monotonicity,[status(thm)],[2131])).
% 1.29/1.47 tff(2133,plain,
% 1.29/1.47 (((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181)))) <=> ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2132, 2130])).
% 1.29/1.48 tff(2134,plain,
% 1.29/1.48 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp34 | hskp33 | (~ndr1_0) | c1_1(a2181) | (~c0_1(a2181)) | (~c2_1(a2181)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2135,plain,
% 1.29/1.48 ((~![U: $i] : (hskp34 | hskp33 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp34 | hskp33 | (~c0_1(a2181)) | c1_1(a2181) | (~c2_1(a2181)) | (~ndr1_0)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 1.29/1.48 tff(2136,plain,
% 1.29/1.48 (hskp34 | (~c0_1(a2181)) | c1_1(a2181)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2135, 150, 72, 1736, 462])).
% 1.29/1.48 tff(2137,plain,
% 1.29/1.48 (hskp34),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2136, 2129, 2121])).
% 1.29/1.48 tff(2138,plain,
% 1.29/1.48 (~c0_1(a2189)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[697, 2137])).
% 1.29/1.48 tff(2139,plain,
% 1.29/1.48 (c3_1(a2189)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[676, 2137])).
% 1.29/1.48 tff(2140,plain,
% 1.29/1.48 (c1_1(a2189)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[684, 2137])).
% 1.29/1.48 tff(2141,plain,
% 1.29/1.48 (~c2_1(a2189)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[718, 150, 72, 2140, 2139, 2138, 71])).
% 1.29/1.48 tff(2142,plain,
% 1.29/1.48 (c3_1(a2181)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[809, 150, 72, 2140, 2138, 2121, 2129, 246, 2141])).
% 1.29/1.48 tff(2143,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2144,plain,
% 1.29/1.48 (((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189))) <=> (c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2145,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | (c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2144])).
% 1.29/1.48 tff(2146,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2145, 2143])).
% 1.29/1.48 tff(2147,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2181)) | (~c0_1(a2181)) | (~c2_1(a2181)) | c0_1(a2189) | c2_1(a2189) | (~c1_1(a2189)) | c0_1(a2189) | c2_1(a2189) | (~c3_1(a2189)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2148,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c3_1(W)))) | c0_1(a2189) | (~c0_1(a2181)) | (~c2_1(a2181)) | (~ndr1_0) | (~c3_1(a2181)) | c2_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.29/1.48 tff(2149,plain,
% 1.29/1.48 ($false),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2148, 150, 2140, 2139, 2138, 2121, 1736, 302, 2142, 2141])).
% 1.29/1.48 tff(2150,plain,(hskp33), inference(lemma,lemma(discharge,[]))).
% 1.29/1.48 tff(2151,plain,
% 1.29/1.48 (~c2_1(a2188)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1044, 2150])).
% 1.29/1.48 tff(2152,plain,
% 1.29/1.48 (~c3_1(a2188)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1050, 2150])).
% 1.29/1.48 tff(2153,plain,
% 1.29/1.48 (c1_1(a2188)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1058, 2150])).
% 1.29/1.48 tff(2154,plain,
% 1.29/1.48 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2155,plain,
% 1.29/1.48 ((hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188))) <=> (hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2156,plain,
% 1.29/1.48 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2155])).
% 1.29/1.48 tff(2157,plain,
% 1.29/1.48 (((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)))) <=> ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2156, 2154])).
% 1.29/1.48 tff(2158,plain,
% 1.29/1.48 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | (hskp18 | (~ndr1_0) | c2_1(a2188) | c3_1(a2188) | (~c1_1(a2188)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2159,plain,
% 1.29/1.48 ((~![U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)))) | hskp18 | c3_1(a2188) | c2_1(a2188) | (~ndr1_0) | (~c1_1(a2188))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 1.29/1.48 tff(2160,plain,
% 1.29/1.48 (hskp18),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2159, 150, 2153, 2152, 2151, 61])).
% 1.29/1.48 tff(2161,plain,
% 1.29/1.48 (hskp32),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1655, 2160])).
% 1.29/1.48 tff(2162,plain,
% 1.29/1.48 (~c2_1(a2186)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[324, 2161])).
% 1.29/1.48 tff(2163,plain,
% 1.29/1.48 (~c3_1(a2186)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[86, 2161])).
% 1.29/1.48 tff(2164,plain,
% 1.29/1.48 (c0_1(a2222)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[423, 2160])).
% 1.29/1.48 tff(2165,plain,
% 1.29/1.48 (c3_1(a2222)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[390, 2160])).
% 1.29/1.48 tff(2166,plain,
% 1.29/1.48 (~c2_1(a2222)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[352, 2160])).
% 1.29/1.48 tff(2167,plain,
% 1.29/1.48 (~c1_1(a2222)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[1612, 2166, 2165, 2164])).
% 1.29/1.48 tff(2168,plain,
% 1.29/1.48 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2169,plain,
% 1.29/1.48 ((hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222))) <=> (hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2170,plain,
% 1.29/1.48 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2169])).
% 1.29/1.48 tff(2171,plain,
% 1.29/1.48 (((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)))) <=> ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2170, 2168])).
% 1.29/1.48 tff(2172,plain,
% 1.29/1.48 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp58 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2173,plain,
% 1.29/1.48 ((~![U: $i] : (hskp58 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp58 | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.29/1.48 tff(2174,plain,
% 1.29/1.48 (hskp58),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2173, 150, 2165, 2166, 121, 2167])).
% 1.29/1.48 tff(2175,plain,
% 1.29/1.48 (~c1_1(a2252)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[163, 2174])).
% 1.29/1.48 tff(2176,plain,
% 1.29/1.48 (~c2_1(a2252)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[169, 2174])).
% 1.29/1.48 tff(2177,plain,
% 1.29/1.48 (c0_1(a2186)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[80, 2161])).
% 1.29/1.48 tff(2178,assumption,(hskp46), introduced(assumption)).
% 1.29/1.48 tff(2179,plain,
% 1.29/1.48 (c2_1(a2218)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[436, 2178])).
% 1.29/1.48 tff(2180,plain,
% 1.29/1.48 (c0_1(a2218)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[444, 2178])).
% 1.29/1.48 tff(2181,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2182,plain,
% 1.29/1.48 (((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218))) <=> (c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2183,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2182])).
% 1.29/1.48 tff(2184,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2183, 2181])).
% 1.29/1.48 tff(2185,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)) | c1_1(a2252) | c2_1(a2252) | (~c3_1(a2252)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c1_1(a2218)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2186,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c0_1(W)) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a2252) | c1_1(a2252) | c3_1(a2186) | c2_1(a2186) | (~ndr1_0) | (~c0_1(a2186)) | (~c1_1(a2218)) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c3_1(a2252))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 1.29/1.48 tff(2187,plain,
% 1.29/1.48 (~c1_1(a2218)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2186, 150, 2180, 2179, 2177, 2176, 2175, 2163, 2162, 51, 21])).
% 1.29/1.48 tff(2188,plain,
% 1.29/1.48 (((~hskp46) | (~c3_1(a2218))) <=> ((~hskp46) | (~c3_1(a2218)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2189,plain,
% 1.29/1.48 (((~c3_1(a2218)) | (~hskp46)) <=> ((~hskp46) | (~c3_1(a2218)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2190,axiom,((~c3_1(a2218)) | (~hskp46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.29/1.48 tff(2191,plain,
% 1.29/1.48 ((~hskp46) | (~c3_1(a2218))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 1.29/1.48 tff(2192,plain,
% 1.29/1.48 ((~hskp46) | (~c3_1(a2218))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2191, 2188])).
% 1.29/1.48 tff(2193,plain,
% 1.29/1.48 (~c3_1(a2218)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2192, 2178])).
% 1.29/1.48 tff(2194,plain,
% 1.29/1.48 (^[V: $i, U: $i] : refl((hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(2195,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[2194])).
% 1.29/1.48 tff(2196,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2197,plain,
% 1.29/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp56))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp56) <=> (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56) <=> (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(2198,plain,
% 1.29/1.48 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[2197])).
% 1.29/1.48 tff(2199,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause276')).
% 1.29/1.48 tff(2200,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2199, 2198])).
% 1.29/1.48 tff(2201,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2200, 2196])).
% 1.29/1.48 tff(2202,plain,(
% 1.29/1.48 ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(skolemize,[status(sab)],[2201])).
% 1.29/1.48 tff(2203,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2202, 2195])).
% 1.29/1.48 tff(2204,plain,
% 1.29/1.48 (c0_1(a2252)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[177, 2174])).
% 1.29/1.48 tff(2205,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2206,plain,
% 1.29/1.48 ((hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2207,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2206])).
% 1.29/1.48 tff(2208,plain,
% 1.29/1.48 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2207, 2205])).
% 1.29/1.48 tff(2209,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2210,plain,
% 1.29/1.48 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | (~c0_1(a2252))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2209, 2208])).
% 1.29/1.48 tff(2211,plain,
% 1.29/1.48 (hskp56),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2210, 150, 2204, 2180, 2179, 2176, 2175, 2203, 2187])).
% 1.29/1.48 tff(2212,plain,
% 1.29/1.48 (((~hskp56) | (~c1_1(a2242))) <=> ((~hskp56) | (~c1_1(a2242)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2213,plain,
% 1.29/1.48 (((~c1_1(a2242)) | (~hskp56)) <=> ((~hskp56) | (~c1_1(a2242)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2214,axiom,((~c1_1(a2242)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.29/1.48 tff(2215,plain,
% 1.29/1.48 ((~hskp56) | (~c1_1(a2242))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 1.29/1.48 tff(2216,plain,
% 1.29/1.48 ((~hskp56) | (~c1_1(a2242))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2215, 2212])).
% 1.29/1.48 tff(2217,plain,
% 1.29/1.48 (~c1_1(a2242)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2216, 2211])).
% 1.29/1.48 tff(2218,plain,
% 1.29/1.48 (((~hskp56) | c2_1(a2242)) <=> ((~hskp56) | c2_1(a2242))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2219,axiom,((~hskp56) | c2_1(a2242)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.29/1.48 tff(2220,plain,
% 1.29/1.48 ((~hskp56) | c2_1(a2242)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 1.29/1.48 tff(2221,plain,
% 1.29/1.48 ((~hskp56) | c2_1(a2242)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2220, 2218])).
% 1.29/1.48 tff(2222,plain,
% 1.29/1.48 ((~hskp56) | c2_1(a2242)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2221, 2218])).
% 1.29/1.48 tff(2223,plain,
% 1.29/1.48 ((~hskp56) | c2_1(a2242)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2222, 2218])).
% 1.29/1.48 tff(2224,plain,
% 1.29/1.48 ((~hskp56) | c2_1(a2242)),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2223, 2218])).
% 1.29/1.48 tff(2225,plain,
% 1.29/1.48 (c2_1(a2242)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2224, 2211])).
% 1.29/1.48 tff(2226,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2227,plain,
% 1.29/1.48 (((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218))) <=> (c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.29/1.48 tff(2228,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242))))),
% 1.29/1.48 inference(monotonicity,[status(thm)],[2227])).
% 1.29/1.48 tff(2229,plain,
% 1.29/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242)))),
% 1.29/1.48 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.29/1.48 tff(2230,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c1_1(a2242) | c0_1(a2242) | (~c2_1(a2242)) | c3_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c3_1(a2218) | c1_1(a2218) | (~c0_1(a2218)))),
% 1.29/1.48 inference(quant_inst,[status(thm)],[])).
% 1.29/1.48 tff(2231,plain,
% 1.29/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a2242) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c2_1(a2218)) | c0_1(a2242) | (~c2_1(a2242))),
% 1.29/1.48 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.29/1.48 tff(2232,plain,
% 1.29/1.48 (c0_1(a2242)),
% 1.29/1.48 inference(unit_resolution,[status(thm)],[2231, 150, 2225, 2180, 2179, 2217, 2193, 974, 2187])).
% 1.29/1.48 tff(2233,plain,
% 1.29/1.48 (^[V: $i, U: $i] : refl((hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.29/1.48 inference(bind,[status(th)],[])).
% 1.29/1.48 tff(2234,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(quant_intro,[status(thm)],[2233])).
% 1.29/1.48 tff(2235,plain,
% 1.29/1.48 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.29/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(2236,plain,
% 1.32/1.48 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp40))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp40) <=> (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40) <=> (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(2237,plain,
% 1.32/1.48 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40) <=> ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[2236])).
% 1.32/1.48 tff(2238,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause267')).
% 1.32/1.48 tff(2239,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 1.32/1.48 tff(2240,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[2239, 2235])).
% 1.32/1.48 tff(2241,plain,(
% 1.32/1.48 ![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.32/1.48 inference(skolemize,[status(sab)],[2240])).
% 1.32/1.48 tff(2242,plain,
% 1.32/1.48 (![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[2241, 2234])).
% 1.32/1.48 tff(2243,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(2244,plain,
% 1.32/1.48 ((hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218))) <=> (hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(2245,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[2244])).
% 1.32/1.48 tff(2246,plain,
% 1.32/1.48 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252)))),
% 1.32/1.48 inference(transitivity,[status(thm)],[2245, 2243])).
% 1.32/1.48 tff(2247,plain,
% 1.32/1.48 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c3_1(a2252)) | c1_1(a2218) | c3_1(a2218) | (~c0_1(a2218)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2248,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c2_1(a2252) | c1_1(a2252) | c3_1(a2218) | (~ndr1_0) | c1_1(a2218) | (~c0_1(a2218)) | (~c3_1(a2252))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 1.32/1.49 tff(2249,plain,
% 1.32/1.49 (hskp40),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2248, 150, 2180, 2176, 2175, 2193, 2242, 21, 2187])).
% 1.32/1.49 tff(2250,plain,
% 1.32/1.49 (((~hskp40) | (~c1_1(a2204))) <=> ((~hskp40) | (~c1_1(a2204)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2251,plain,
% 1.32/1.49 (((~c1_1(a2204)) | (~hskp40)) <=> ((~hskp40) | (~c1_1(a2204)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2252,axiom,((~c1_1(a2204)) | (~hskp40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 1.32/1.49 tff(2253,plain,
% 1.32/1.49 ((~hskp40) | (~c1_1(a2204))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 1.32/1.49 tff(2254,plain,
% 1.32/1.49 ((~hskp40) | (~c1_1(a2204))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2253, 2250])).
% 1.32/1.49 tff(2255,plain,
% 1.32/1.49 (~c1_1(a2204)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2254, 2249])).
% 1.32/1.49 tff(2256,plain,
% 1.32/1.49 (((~hskp56) | (~c3_1(a2242))) <=> ((~hskp56) | (~c3_1(a2242)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2257,plain,
% 1.32/1.49 (((~c3_1(a2242)) | (~hskp56)) <=> ((~hskp56) | (~c3_1(a2242)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2258,axiom,((~c3_1(a2242)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.32/1.49 tff(2259,plain,
% 1.32/1.49 ((~hskp56) | (~c3_1(a2242))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 1.32/1.49 tff(2260,plain,
% 1.32/1.49 ((~hskp56) | (~c3_1(a2242))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2259, 2256])).
% 1.32/1.49 tff(2261,plain,
% 1.32/1.49 (~c3_1(a2242)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2260, 2211])).
% 1.32/1.49 tff(2262,plain,
% 1.32/1.49 (((~hskp40) | c3_1(a2204)) <=> ((~hskp40) | c3_1(a2204))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2263,axiom,((~hskp40) | c3_1(a2204)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.32/1.49 tff(2264,plain,
% 1.32/1.49 ((~hskp40) | c3_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 1.32/1.49 tff(2265,plain,
% 1.32/1.49 ((~hskp40) | c3_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2264, 2262])).
% 1.32/1.49 tff(2266,plain,
% 1.32/1.49 ((~hskp40) | c3_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2265, 2262])).
% 1.32/1.49 tff(2267,plain,
% 1.32/1.49 ((~hskp40) | c3_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2266, 2262])).
% 1.32/1.49 tff(2268,plain,
% 1.32/1.49 ((~hskp40) | c3_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2267, 2262])).
% 1.32/1.49 tff(2269,plain,
% 1.32/1.49 (c3_1(a2204)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2268, 2249])).
% 1.32/1.49 tff(2270,plain,
% 1.32/1.49 (((~hskp40) | c2_1(a2204)) <=> ((~hskp40) | c2_1(a2204))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2271,axiom,((~hskp40) | c2_1(a2204)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.32/1.49 tff(2272,plain,
% 1.32/1.49 ((~hskp40) | c2_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.32/1.49 tff(2273,plain,
% 1.32/1.49 ((~hskp40) | c2_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2272, 2270])).
% 1.32/1.49 tff(2274,plain,
% 1.32/1.49 ((~hskp40) | c2_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2273, 2270])).
% 1.32/1.49 tff(2275,plain,
% 1.32/1.49 ((~hskp40) | c2_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2274, 2270])).
% 1.32/1.49 tff(2276,plain,
% 1.32/1.49 ((~hskp40) | c2_1(a2204)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2275, 2270])).
% 1.32/1.49 tff(2277,plain,
% 1.32/1.49 (c2_1(a2204)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2276, 2249])).
% 1.32/1.49 tff(2278,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2279,plain,
% 1.32/1.49 ((hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204))) <=> (hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2280,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[2279])).
% 1.32/1.49 tff(2281,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2280, 2278])).
% 1.32/1.49 tff(2282,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2242) | c3_1(a2242) | (~c2_1(a2242)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2283,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp3 | c1_1(a2242) | c3_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2242))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.32/1.49 tff(2284,plain,
% 1.32/1.49 (hskp3),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2283, 150, 2225, 2277, 2269, 2217, 2261, 2255, 20])).
% 1.32/1.49 tff(2285,plain,
% 1.32/1.49 (((~hskp3) | (~c0_1(a2190))) <=> ((~hskp3) | (~c0_1(a2190)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2286,plain,
% 1.32/1.49 (((~c0_1(a2190)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a2190)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2287,axiom,((~c0_1(a2190)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 1.32/1.49 tff(2288,plain,
% 1.32/1.49 ((~hskp3) | (~c0_1(a2190))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 1.32/1.49 tff(2289,plain,
% 1.32/1.49 ((~hskp3) | (~c0_1(a2190))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2288, 2285])).
% 1.32/1.49 tff(2290,plain,
% 1.32/1.49 (~c0_1(a2190)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2289, 2284])).
% 1.32/1.49 tff(2291,plain,
% 1.32/1.49 (((~hskp3) | (~c1_1(a2190))) <=> ((~hskp3) | (~c1_1(a2190)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2292,plain,
% 1.32/1.49 (((~c1_1(a2190)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a2190)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2293,axiom,((~c1_1(a2190)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause234')).
% 1.32/1.49 tff(2294,plain,
% 1.32/1.49 ((~hskp3) | (~c1_1(a2190))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 1.32/1.49 tff(2295,plain,
% 1.32/1.49 ((~hskp3) | (~c1_1(a2190))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2294, 2291])).
% 1.32/1.49 tff(2296,plain,
% 1.32/1.49 (~c1_1(a2190)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2295, 2284])).
% 1.32/1.49 tff(2297,plain,
% 1.32/1.49 (((~hskp3) | c2_1(a2190)) <=> ((~hskp3) | c2_1(a2190))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2298,axiom,((~hskp3) | c2_1(a2190)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.32/1.49 tff(2299,plain,
% 1.32/1.49 ((~hskp3) | c2_1(a2190)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.32/1.49 tff(2300,plain,
% 1.32/1.49 ((~hskp3) | c2_1(a2190)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2299, 2297])).
% 1.32/1.49 tff(2301,plain,
% 1.32/1.49 ((~hskp3) | c2_1(a2190)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2300, 2297])).
% 1.32/1.49 tff(2302,plain,
% 1.32/1.49 ((~hskp3) | c2_1(a2190)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2301, 2297])).
% 1.32/1.49 tff(2303,plain,
% 1.32/1.49 ((~hskp3) | c2_1(a2190)),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2302, 2297])).
% 1.32/1.49 tff(2304,plain,
% 1.32/1.49 (c2_1(a2190)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2303, 2284])).
% 1.32/1.49 tff(2305,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2306,plain,
% 1.32/1.49 (((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186))) <=> (c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2307,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[2306])).
% 1.32/1.49 tff(2308,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2307, 2305])).
% 1.32/1.49 tff(2309,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)) | c2_1(a2186) | c3_1(a2186) | (~c0_1(a2186)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2310,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2242) | c3_1(a2186) | c2_1(a2186) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c2_1(a2190)) | (~c0_1(a2186)) | (~c0_1(a2242)) | (~c2_1(a2242))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 1.32/1.49 tff(2311,plain,
% 1.32/1.49 ($false),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2310, 150, 2225, 2177, 2304, 2261, 2163, 2162, 2296, 2290, 559, 2232])).
% 1.32/1.49 tff(2312,plain,((~hskp46) | (~c3_1(a2252))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.49 tff(2313,plain,
% 1.32/1.49 (~hskp46),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2312, 21])).
% 1.32/1.49 tff(2314,plain,
% 1.32/1.49 (hskp46 | hskp34),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[427, 150, 2164, 2165, 416, 2167])).
% 1.32/1.49 tff(2315,plain,
% 1.32/1.49 (hskp34),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2314, 2313])).
% 1.32/1.49 tff(2316,plain,
% 1.32/1.49 (~c0_1(a2189)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[697, 2315])).
% 1.32/1.49 tff(2317,plain,
% 1.32/1.49 (hskp44),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[1629, 150, 2164, 2165, 2166, 1623, 2167])).
% 1.32/1.49 tff(2318,plain,
% 1.32/1.49 (~c0_1(a2215)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[1635, 2317])).
% 1.32/1.49 tff(2319,plain,
% 1.32/1.49 (c3_1(a2189)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[676, 2315])).
% 1.32/1.49 tff(2320,plain,
% 1.32/1.49 (c1_1(a2189)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[684, 2315])).
% 1.32/1.49 tff(2321,plain,
% 1.32/1.49 (c1_1(a2215)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[1643, 2317])).
% 1.32/1.49 tff(2322,plain,
% 1.32/1.49 (c2_1(a2215)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[1651, 2317])).
% 1.32/1.49 tff(2323,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2324,plain,
% 1.32/1.49 ((hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189))) <=> (hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2325,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[2324])).
% 1.32/1.49 tff(2326,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))) <=> ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2325, 2323])).
% 1.32/1.49 tff(2327,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp48 | (~ndr1_0) | c0_1(a2215) | (~c1_1(a2215)) | (~c2_1(a2215)) | c0_1(a2189) | (~c3_1(a2189)) | (~c1_1(a2189)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2328,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp48 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp48 | c0_1(a2215) | c0_1(a2189) | (~ndr1_0) | (~c3_1(a2189)) | (~c1_1(a2189)) | (~c2_1(a2215)) | (~c1_1(a2215))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 1.32/1.49 tff(2329,plain,
% 1.32/1.49 (hskp48),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2328, 150, 2322, 2321, 2320, 2319, 2318, 2316, 41])).
% 1.32/1.49 tff(2330,plain,
% 1.32/1.49 (~c0_1(a2228)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[1110, 2329])).
% 1.32/1.49 tff(2331,plain,
% 1.32/1.49 (c2_1(a2228)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[1118, 2329])).
% 1.32/1.49 tff(2332,plain,
% 1.32/1.49 (c3_1(a2228)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[1126, 2329])).
% 1.32/1.49 tff(2333,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2334,plain,
% 1.32/1.49 ((hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252))) <=> (hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2335,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[2334])).
% 1.32/1.49 tff(2336,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2335, 2333])).
% 1.32/1.49 tff(2337,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | (hskp40 | (~ndr1_0) | c0_1(a2228) | (~c3_1(a2228)) | (~c2_1(a2228)) | c2_1(a2252) | (~c0_1(a2252)) | (~c3_1(a2252)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2338,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)))) | hskp40 | c2_1(a2252) | c0_1(a2228) | (~ndr1_0) | (~c2_1(a2228)) | (~c3_1(a2228)) | (~c3_1(a2252)) | (~c0_1(a2252))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2337, 2336])).
% 1.32/1.49 tff(2339,plain,
% 1.32/1.49 (hskp40),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2338, 150, 2204, 2332, 2331, 2176, 2330, 31, 21])).
% 1.32/1.49 tff(2340,plain,
% 1.32/1.49 (~c1_1(a2204)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2254, 2339])).
% 1.32/1.49 tff(2341,plain,
% 1.32/1.49 (c2_1(a2204)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2276, 2339])).
% 1.32/1.49 tff(2342,plain,
% 1.32/1.49 (c3_1(a2204)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2268, 2339])).
% 1.32/1.49 tff(2343,assumption,(~c0_1(a2204)), introduced(assumption)).
% 1.32/1.49 tff(2344,assumption,(~c1_1(a2204)), introduced(assumption)).
% 1.32/1.49 tff(2345,assumption,(c3_1(a2204)), introduced(assumption)).
% 1.32/1.49 tff(2346,assumption,(c2_1(a2204)), introduced(assumption)).
% 1.32/1.49 tff(2347,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2348,plain,
% 1.32/1.49 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204))) <=> (c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2349,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[2348])).
% 1.32/1.49 tff(2350,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2349, 2347])).
% 1.32/1.49 tff(2351,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | c1_1(a2204) | (~c2_1(a2204)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2352,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2204) | (~c0_1(a2252))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 1.32/1.49 tff(2353,plain,
% 1.32/1.49 ($false),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2352, 150, 2204, 2346, 2345, 2176, 2175, 2344, 10, 2343])).
% 1.32/1.49 tff(2354,plain,(c0_1(a2204) | (~c2_1(a2204)) | (~c3_1(a2204)) | c1_1(a2204)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.49 tff(2355,plain,
% 1.32/1.49 (c0_1(a2204)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2354, 2340, 2342, 2341])).
% 1.32/1.49 tff(2356,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2357,plain,
% 1.32/1.49 ((hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252))) <=> (hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2358,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[2357])).
% 1.32/1.49 tff(2359,plain,
% 1.32/1.49 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2358, 2356])).
% 1.32/1.49 tff(2360,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp56 | (~ndr1_0) | c1_1(a2204) | (~c0_1(a2204)) | (~c2_1(a2204)) | c1_1(a2252) | c2_1(a2252) | (~c0_1(a2252)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2361,plain,
% 1.32/1.49 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp56 | c2_1(a2252) | c1_1(a2252) | c1_1(a2204) | (~ndr1_0) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c0_1(a2252))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 1.32/1.49 tff(2362,plain,
% 1.32/1.49 (hskp56),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2361, 150, 2204, 2341, 2176, 2175, 2340, 2203, 2355])).
% 1.32/1.49 tff(2363,plain,
% 1.32/1.49 (~c3_1(a2242)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2260, 2362])).
% 1.32/1.49 tff(2364,plain,
% 1.32/1.49 (~c1_1(a2242)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2216, 2362])).
% 1.32/1.49 tff(2365,plain,
% 1.32/1.49 (c2_1(a2242)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2224, 2362])).
% 1.32/1.49 tff(2366,plain,
% 1.32/1.49 (hskp3),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2283, 150, 2365, 2341, 2342, 2364, 2363, 2340, 20])).
% 1.32/1.49 tff(2367,plain,
% 1.32/1.49 (~c0_1(a2190)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2289, 2366])).
% 1.32/1.49 tff(2368,plain,
% 1.32/1.49 (~c1_1(a2190)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2295, 2366])).
% 1.32/1.49 tff(2369,plain,
% 1.32/1.49 (c2_1(a2190)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2303, 2366])).
% 1.32/1.49 tff(2370,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2371,plain,
% 1.32/1.49 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190))) <=> (c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2372,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[2371])).
% 1.32/1.49 tff(2373,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252)))),
% 1.32/1.49 inference(transitivity,[status(thm)],[2372, 2370])).
% 1.32/1.49 tff(2374,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2190) | (~c3_1(a2190)) | (~c2_1(a2190)) | c0_1(a2190) | c1_1(a2190) | (~c2_1(a2190)))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(2375,plain,
% 1.32/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2190) | c0_1(a2190) | (~ndr1_0) | (~c3_1(a2190)) | (~c2_1(a2190)) | (~c0_1(a2252))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.32/1.49 tff(2376,plain,
% 1.32/1.49 (~c3_1(a2190)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[2375, 150, 2204, 2369, 2176, 2175, 2368, 2367, 10])).
% 1.32/1.49 tff(2377,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2378,plain,
% 1.32/1.49 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228))) <=> (c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(2379,plain,
% 1.32/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2378])).
% 1.32/1.50 tff(2380,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2379, 2377])).
% 1.32/1.50 tff(2381,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2228) | c1_1(a2228) | (~c2_1(a2228)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2382,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c0_1(a2228) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c2_1(a2228)) | c1_1(a2228) | (~c0_1(a2252))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2381, 2380])).
% 1.32/1.50 tff(2383,plain,
% 1.32/1.50 (c1_1(a2228)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2382, 150, 2204, 2331, 2341, 2342, 2176, 2175, 2330, 2340, 10])).
% 1.32/1.50 tff(2384,plain,
% 1.32/1.50 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(2385,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[2384])).
% 1.32/1.50 tff(2386,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2387,plain,
% 1.32/1.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W)))), ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W))))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(2388,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[2387])).
% 1.32/1.50 tff(2389,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c3_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause296')).
% 1.32/1.50 tff(2390,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 1.32/1.50 tff(2391,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2390, 2386])).
% 1.32/1.50 tff(2392,plain,(
% 1.32/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.32/1.50 inference(skolemize,[status(sab)],[2391])).
% 1.32/1.50 tff(2393,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2392, 2385])).
% 1.32/1.50 tff(2394,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2395,plain,
% 1.32/1.50 (((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190))) <=> (c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2396,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2395])).
% 1.32/1.50 tff(2397,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2396, 2394])).
% 1.32/1.50 tff(2398,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a2228) | (~c1_1(a2228)) | (~c3_1(a2228)) | (~c0_1(a2204)) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2190) | c3_1(a2190) | (~c2_1(a2190)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2399,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2228) | c0_1(a2190) | (~ndr1_0) | c3_1(a2190) | (~c2_1(a2190)) | (~c3_1(a2204)) | (~c2_1(a2204)) | (~c0_1(a2204)) | (~c1_1(a2228)) | (~c3_1(a2228))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 1.32/1.50 tff(2400,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2399, 150, 2332, 2341, 2342, 2369, 2330, 2367, 2393, 2355, 2383, 2376])).
% 1.32/1.50 tff(2401,plain,(~c3_1(a2252)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(2402,plain,
% 1.32/1.50 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(2403,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[2402])).
% 1.32/1.50 tff(2404,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2405,plain,
% 1.32/1.50 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W)))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W)))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c2_1(W) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(2406,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[2405])).
% 1.32/1.50 tff(2407,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c3_1(W)) | c2_1(W)) | c0_1(W)) | c2_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause285')).
% 1.32/1.50 tff(2408,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2407, 2406])).
% 1.32/1.50 tff(2409,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2408, 2404])).
% 1.32/1.50 tff(2410,plain,(
% 1.32/1.50 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 1.32/1.50 inference(skolemize,[status(sab)],[2409])).
% 1.32/1.50 tff(2411,plain,
% 1.32/1.50 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2410, 2403])).
% 1.32/1.50 tff(2412,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2413,plain,
% 1.32/1.50 ((hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252))) <=> (hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2414,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2413])).
% 1.32/1.50 tff(2415,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))) <=> ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2414, 2412])).
% 1.32/1.50 tff(2416,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp40 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c1_1(a2252) | c3_1(a2252) | (~c0_1(a2252)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2417,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp40 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp40 | c1_1(a2252) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2252) | (~c0_1(a2252))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 1.32/1.50 tff(2418,plain,
% 1.32/1.50 (hskp40 | c3_1(a2252)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2417, 150, 2204, 2165, 2175, 2166, 2242, 2167])).
% 1.32/1.50 tff(2419,plain,
% 1.32/1.50 (hskp40),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2418, 2401])).
% 1.32/1.50 tff(2420,plain,
% 1.32/1.50 (c2_1(a2204)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2276, 2419])).
% 1.32/1.50 tff(2421,plain,
% 1.32/1.50 (~c1_1(a2204)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2254, 2419])).
% 1.32/1.50 tff(2422,plain,
% 1.32/1.50 (c3_1(a2204)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2268, 2419])).
% 1.32/1.50 tff(2423,plain,
% 1.32/1.50 (c0_1(a2204)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2354, 2421, 2422, 2420])).
% 1.32/1.50 tff(2424,plain,
% 1.32/1.50 (hskp56),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2361, 150, 2204, 2420, 2176, 2175, 2421, 2203, 2423])).
% 1.32/1.50 tff(2425,plain,
% 1.32/1.50 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(2426,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[2425])).
% 1.32/1.50 tff(2427,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2428,plain,
% 1.32/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(2429,plain,
% 1.32/1.50 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[2428])).
% 1.32/1.50 tff(2430,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | c2_1(U)) | c1_1(U)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause275')).
% 1.32/1.50 tff(2431,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2430, 2429])).
% 1.32/1.50 tff(2432,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2431, 2427])).
% 1.32/1.50 tff(2433,plain,(
% 1.32/1.50 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(skolemize,[status(sab)],[2432])).
% 1.32/1.50 tff(2434,plain,
% 1.32/1.50 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2433, 2426])).
% 1.32/1.50 tff(2435,assumption,(hskp56), introduced(assumption)).
% 1.32/1.50 tff(2436,plain,
% 1.32/1.50 (~c3_1(a2242)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2260, 2435])).
% 1.32/1.50 tff(2437,plain,
% 1.32/1.50 (c2_1(a2242)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2224, 2435])).
% 1.32/1.50 tff(2438,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2439,plain,
% 1.32/1.50 ((hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242))) <=> (hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2440,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2439])).
% 1.32/1.50 tff(2441,plain,
% 1.32/1.50 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2440, 2438])).
% 1.32/1.50 tff(2442,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a2222) | c1_1(a2222) | (~c3_1(a2222)) | c3_1(a2242) | (~c0_1(a2242)) | (~c2_1(a2242)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2443,plain,
% 1.32/1.50 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp10 | c3_1(a2242) | c2_1(a2222) | (~ndr1_0) | c1_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2242)) | (~c2_1(a2242))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 1.32/1.50 tff(2444,plain,
% 1.32/1.50 (~c0_1(a2242)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2443, 150, 1793, 2437, 2165, 2436, 2166, 2434, 2167])).
% 1.32/1.50 tff(2445,plain,
% 1.32/1.50 (~c1_1(a2242)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2216, 2435])).
% 1.32/1.50 tff(2446,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2447,plain,
% 1.32/1.50 (((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242))) <=> (c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2448,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2447])).
% 1.32/1.50 tff(2449,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252)))),
% 1.32/1.50 inference(transitivity,[status(thm)],[2448, 2446])).
% 1.32/1.50 tff(2450,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2252) | c1_1(a2252) | (~c0_1(a2252)) | c1_1(a2204) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | c1_1(a2242) | (~c2_1(a2242)))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(2451,plain,
% 1.32/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a2252) | c1_1(a2252) | c1_1(a2242) | c1_1(a2204) | (~ndr1_0) | (~c3_1(a2204)) | (~c2_1(a2204)) | c0_1(a2242) | (~c2_1(a2242)) | (~c0_1(a2252))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 1.32/1.50 tff(2452,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2451, 150, 2204, 2437, 2346, 2345, 2176, 2175, 2445, 2344, 10, 2444])).
% 1.32/1.50 tff(2453,plain,((~hskp56) | (~c2_1(a2204)) | (~c3_1(a2204)) | c1_1(a2204) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(2454,plain,
% 1.32/1.50 (hskp10),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[2453, 2424, 2422, 2421, 2420])).
% 1.32/1.50 tff(2455,plain,
% 1.32/1.50 (~c3_1(a2206)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1550, 2454])).
% 1.32/1.50 tff(2456,plain,
% 1.32/1.50 (~c0_1(a2206)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1569, 2454])).
% 1.32/1.50 tff(2457,plain,
% 1.32/1.50 (~c2_1(a2206)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1556, 2454])).
% 1.32/1.50 tff(2458,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | (c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2459,plain,
% 1.32/1.50 (((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206)) <=> (c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(2460,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | (c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252)))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[2459])).
% 1.32/1.50 tff(2461,plain,
% 1.32/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252))),
% 1.32/1.51 inference(transitivity,[status(thm)],[2460, 2458])).
% 1.32/1.51 tff(2462,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2222) | (~c3_1(a2222)) | (~c0_1(a2222)) | c1_1(a2252) | c3_1(a2252) | c2_1(a2252) | c0_1(a2206) | c2_1(a2206) | c3_1(a2206))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(2463,plain,
% 1.32/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | c2_1(V) | c0_1(W) | c2_1(W) | c3_1(W))) | c2_1(a2252) | c1_1(a2252) | c2_1(a2222) | c2_1(a2206) | c0_1(a2206) | c3_1(a2206) | (~ndr1_0) | (~c3_1(a2222)) | (~c0_1(a2222)) | c3_1(a2252)),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 1.32/1.51 tff(2464,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[2463, 150, 2164, 2165, 2176, 2175, 2166, 2457, 2456, 2455, 2411, 2401])).
% 1.32/1.51 % SZS output end Proof
% 1.32/1.52 % E exiting
%------------------------------------------------------------------------------